HSN.VM.A.1Common CoreMathNumber and QuantityGrades 9-12
HSN.VM.A.1: Vector Quantities, Directed Line Segments and Vector Notation
In plain English: HSN.VM.A.1 is an advanced (+) Common Core number and quantity standard that asks students to recognize vector quantities, such as velocity or force, as having both a magnitude and a direction. Students draw vectors as directed line segments from an initial point to a terminal point and use standard symbols: a bold v for the vector and |v|, ||v|| or an italic v for its magnitude. It is usually taught in Precalculus.
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., bold v, |v|, ||v||, and italic v).
Common Core State Standards for Mathematics · Domain: Vector and Matrix Quantities (VM) · Cluster: Represent and model with vector quantities. Also written as HSN-VM.A.1 or N-VM.1 · Official standard
Students learn that some quantities, such as speed, mass and temperature, are fully described by one number with a unit, while others, such as velocity, force and displacement, also need a direction. The second kind are vector quantities. Students draw vectors as directed line segments whose length shows the magnitude at a chosen scale and whose arrowhead shows the direction, and they give that direction as an angle from the positive x-direction or as a compass bearing.
Notation used on this page. A bold letter such as v names a vector. Its magnitude is written |v|, ||v|| or as the same letter in italics, v; each of these is a nonnegative number with a unit, not a vector. The vector from point A to point B is written AB in bold, while AB in plain type is the length of the segment. Bold is hard to write by hand, so on paper students draw a small arrow over the letter instead.
Learning Objectives
By the end of this lesson, students will be able to:
Classify quantities as scalar or vector and name the magnitude and direction of a vector quantity
Represent a vector quantity by a directed line segment drawn to a stated scale, with its initial and terminal points marked
Describe a direction as an angle from the positive x-direction or as a compass bearing, and convert between the two
Use the symbols bold v, |v|, ||v|| and italic v correctly, and recognize equal and opposite vectors
Prior Knowledge Required
Students should already be comfortable with:
Measuring and drawing angles with a protractor, and scale drawings 7.G.A.1
The Pythagorean theorem for distances on a coordinate grid 8.G.B.8
Units of measure and choosing a scale HSN.Q.A.1
Right-triangle trigonometry for angles in a grid triangle HSG.SRT.C.8
Show a simple map of a town with the school in the center and ask the question below. Give students two minutes to talk with a partner before sharing.
Warm-Up Prompt
"Maya and Leo each leave school and each end up exactly 3 miles away from it, measured in a straight line. Must they be at the same place? What one extra piece of information would let you find each of them on the map?"
Students should notice that 3 miles only tells how far, and that Maya could be 3 miles north while Leo is 3 miles southeast. The missing piece is a direction. Write two words on the board: magnitude (how much) and direction (which way). Tell students that a quantity that needs both is called a vector quantity, and that today they will learn to recognize, draw and name these quantities.
Direct Instruction20 minutes
Part 1: Scalars and vectors. A scalar quantity is described completely by a single number with a unit. A vector quantity has a magnitude and a direction. Many physical quantities come in pairs, one of each kind:
Scalar and vector pairs
Scalar (magnitude only)
Vector (magnitude and direction)
Speed: 65 mph
Velocity: 65 mph due north
Distance: 4 km
Displacement: 4 km southwest of the start
Mass: 12 kg
Weight: about 118 N straight down (12 kg times 9.8 m/s²)
Temperature: 72°F
No vector partner: temperature has no direction
Part 2: Directed line segments. Draw a vector as an arrow. The starting point is the initial point (the tail) and the arrowhead is at the terminal point (the head). The length of the arrow, at a stated scale, shows the magnitude, and the way the arrow points shows the direction. Use Diagram 1: v runs from P(1, 1) to Q(4, 5), so its length is 5 units. Two vectors are equal when they have the same magnitude and the same direction, even if they start at different places, so w = v in the diagram. The vector with the same magnitude as v and the opposite direction is written -v. Directions are usually given in one of two ways, shown in Diagram 2: an angle measured counterclockwise from the positive x-direction, or a compass bearing such as N 60° E (start at north and turn 60° toward east).
Part 3: Symbols. Go through these conventions and have students copy them into their notes:
The vector itself: a bold letter, v, or PQ for the vector from P to Q. By hand, draw an arrow over the letter.
Its magnitude: |v|, ||v|| or italic v. All three mean the same nonnegative number. The double bars help separate the magnitude of a vector from the absolute value of a number.
Equal and opposite: v = w means same magnitude and same direction; -v has the same magnitude as v and points the other way, so |-v| = |v|.
Keep the types apart: a vector is never equal to a plain number, and a magnitude never carries a direction. Write v = 30 m/s east or |v| = 30 m/s, never |v| = 30 m/s east.
Work through the examples below with the class.
Scalar or vector
A forecast says: "wind from the north at 25 km/h." Is the wind a vector? Name its magnitude and direction.
Equation: Vector. Magnitude 25 km/h; the air moves toward the south, because wind is named for where it comes from.
Drawing to scale
A hiker's displacement is 6 km at a bearing of N 30° E. Draw it with the scale 1 cm = 2 km.
Equation: An arrow 6 ÷ 2 = 3 cm long, turned 30° from north toward east (60° counterclockwise from east).
Reading a vector on a grid
Vector v has initial point P(1, 1) and terminal point Q(4, 5), 1 unit per grid square (Diagram 1).
Equation: |v| = √(3² + 4²) = 5 units, pointing up and to the right at about 53.1° from the +x direction.
Equal vectors
On a grid, u runs from A(0, 0) to B(2, 3), and r runs from C(4, 1) to D(6, 4). Is u = r?
Equation: Yes. Both go 2 right and 3 up, so they have the same length √13 and the same direction. Position does not matter.
Writing magnitudes
A force F of 40 newtons points straight up. Write its magnitude in three ways and say what F alone means.
Equation: |F| = ||F|| = F = 40 N. The bold F names the whole force: 40 N, straight up.
Guided Practice15 minutes
Pairs draw three vectors on graph paper with a ruler and protractor, then trade papers and check each other's lengths and angles. Circulate and ask each pair to say the magnitude and direction of each arrow out loud.
Guided practice vectors
Quantity
Scale
Arrow length
Velocity 50 km/h due east
1 cm = 10 km/h
5 cm, pointing right
Force 30 N at 45° from +x
1 cm = 5 N
6 cm, halfway between east and north
Displacement 750 m at bearing S 20° W
1 cm = 150 m
5 cm, 20° from south toward west
Listen for these errors: measuring a bearing from east instead of north, turning the wrong way from north or south, and choosing an arrow length without using the scale. Ask one pair to explain why the 45° force and a 30 N force at 225° are not equal vectors even though their arrows have the same length.
Independent Practice15 minutes
Project a grid where each square stands for 10 m/s and four velocity vectors are drawn: a from (0, 0) to (0, 4), b from (2, 1) to (5, 1), c from (6, 5) to (6, 1) and d from (1, 6) to (4, 6). Students work alone to:
state each magnitude with its unit (a and c: 40 m/s; b and d: 30 m/s)
describe each direction in words and as an angle from +x (a: up, 90°; b and d: right, 0°; c: down, 270°)
name every pair of equal vectors and every pair of opposite vectors, in symbols (b = d and c = -a)
write one sentence explaining why |a| = |c| is true but a = c is false
Closure5 minutes
Exit ticket: (1) "A train moves at 30 m/s." Is this a vector description? If not, add what is missing. (2) Explain in one sentence the difference between v and |v|. (3) Sketch a 20 N force at 120° from the +x direction using the scale 1 cm = 5 N, and state the length of your arrow (4 cm).
Differentiation Strategies
For Struggling Students
Give a two-column organizer with the headings "How much?" and "Which way?" and have students fill both columns before calling a quantity a vector
Provide pre-printed compass roses and protractors marked with N, E, S and W so bearings start from the right line
Let students draw first on a grid with a scale of one square per unit before moving to ruler and protractor drawings
For Advanced Students
Ask why the zero vector has magnitude 0 but no direction, and whether it is a scalar or a vector
Ask students to describe the same direction in three ways (angle from +x, bearing, and words such as "northwest") and decide which ones can be exact
Challenge students to find two different quantities in a sport, such as a kicked ball or a swimmer, that must be described as vectors, and draw each to scale
Assessment Guidance
What to Look For
Check that students give a direction every time they call something a vector, and that they never attach a direction to a magnitude. In drawings, the arrow length should match the scale to within a few millimeters and the angle should be measured from the stated reference line. When students compare two vectors, listen for both conditions: same magnitude and same direction. Equal lengths alone are not enough.
02
Classroom Activities
3 Activities
1
Scalar or Vector Card Sort
15 minPairs
Pairs sort 12 quantity cards into two piles, scalar and vector, then match the cards into scalar-vector partners where they can. The sort makes students ask the key question for every quantity: does it need a direction?
The 12 Cards
Scalar cards: speed of 45 mph; mass of 70 kg; temperature of 18°C; time of 90 s; volume of 2 L; distance of 5 km
Vector cards: velocity of 45 mph west; weight of 686 N straight down; displacement of 2.4 km northeast; a 15 N push toward the east; wind from the south at 30 km/h; acceleration of 9.8 m/s² downward
Procedure
Shuffle the cards (6 scalar, 6 vector) and deal them face up
Pairs place each card in a pile and write one reason on a sticky note, such as "needs a direction"
Pairs then link partner cards: speed with velocity, distance with displacement, mass with weight
For every vector card, students write the magnitude and the direction separately
Discussion Questions
The weight card is 686 N and the mass card is 70 kg. How are they related? (686 = 70 × 9.8.)
Which scalar cards have no vector partner? Why?
Wind "from the south" is moving which way?
Modification for Distance Learning
Put the cards on a shared slide with two labeled boxes. Pairs drag the cards into place in a breakout room, then post their partner matches in the chat.
2
Draw It, Trade It, Read It
20 minPairs
Each partner draws three vectors to scale from written descriptions. Partners trade drawings without the descriptions, and each one measures the other's arrows and writes the description back in words and symbols. A match shows the drawing carried the full magnitude and direction.
Description Cards
Partner A: (1) velocity 240 km/h at bearing N 45° E, scale 1 cm = 40 km/h; (2) force 35 N at 150° from +x, scale 1 cm = 7 N; (3) displacement 1.2 km due south, scale 1 cm = 0.3 km
Partner B: (4) current 3 m/s at bearing S 60° E, scale 1 cm = 0.5 m/s; (5) rope tension 80 N at 210° from +x, scale 1 cm = 20 N; (6) walk of 450 m at bearing N 10° W, scale 1 cm = 90 m
Procedure
Each partner computes each arrow length first (the lengths are 6, 5, 4, 6, 4 and 5 cm), then draws with a ruler and protractor and labels the tail and head
Partners trade drawings and the scale only, measure, and write each vector as a sentence and in symbols, for example |f| = 35 N at 150°
Partners compare with the original cards and fix any mismatch
Discussion Questions
Card 4 uses a bearing and card 5 uses an angle from +x. Rewrite each in the other form.
If a drawing is 2 mm too short, how large is the error in newtons for card 2?
Challenge Variation
Pairs write a description for a vector whose arrow at 1 cm = 25 N must be 4.4 cm long, then draw it at a second scale of their choice and compare the two drawings.
3
Vector Walk and Notation Log
20 minGroups of 3
Groups mark directed line segments on the floor with masking tape (or in chalk outside), walk them, and record each one in a notation log. The physical walk links the arrow on paper to a real displacement, and the log gives practice with the symbols.
Setup
Each group tapes a north arrow on the floor and a start dot labeled O
Each group receives four walks: 4 m north; 3 m east; 4 m south; 5 m at bearing N 37° E (about the diagonal of a 3 m by 4 m rectangle)
Procedure
One student walks, one measures with a tape measure and a paper compass rose, and one records; roles rotate for each walk
For each walk, tape an arrow from start to end and label it s1, s2, s3 or s4
In the log, write each walk as the vector with its direction, and separately as its magnitude, for example |s1| = 4 m
Mark in the log every pair of arrows that are opposite, and every pair with the same magnitude but different directions
Discussion Questions
Which two walks are opposite vectors? How do you write that in symbols?
Two walks have the same length but are not equal. Why not?
Why is it wrong to write |s4| = 5 m at N 37° E?
Modification for Small Rooms
Use a scale of 1 m = 20 cm and tape the arrows on a table or a large sheet of paper instead of the floor.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Parts of a Directed Line Segment
Vector v runs from its initial point P(1, 1) to its terminal point Q(4, 5). The dashed legs are 3 and 4 units, so |v| = 5 units, and the direction angle θ is about 53.1°. Vector w starts at (5, 0) and ends at (8, 4): it has the same length and direction, so w = v. Drawn to scale on a unit grid.
Diagram 2: One Direction, Two Descriptions
The same velocity v, 60 km/h, drawn twice at the scale shown (the arrows are twice the scale bar). On the left its direction is 30° counterclockwise from the +x (east) direction. On the right it is the bearing N 60° E: start at north and turn 60° toward east. Since 90° - 60° = 30°, both describe the same direction.
04
Homework Assignment
~30 min
HSN.VM.A.1 Homework: Vector Quantities and Notation
Directions: Use a ruler, a protractor and graph paper. Give every magnitude with its unit and every direction with its reference line (from +x, or a compass bearing). Write vectors in bold or with an arrow over the letter.
Part 1: Magnitude and Direction (Problems 1-2)
Label each quantity scalar or vector. For each vector, state its magnitude and its direction separately. (a) a hot-air balloon rising at 2 m/s straight up (b) a 5 kg bag of rice (c) a 40 N push toward the west (d) a flight that lasts 3 hours (e) a speedometer reading of 55 mph
A runner completes exactly one lap of a 400 m track in 80 seconds and finishes where she started. (a) What distance did she run, and what is her average speed? (b) What is her displacement for the lap? Explain which of your answers are scalars and which is a vector, and why the vector has no direction.
Part 2: Drawing Directed Line Segments (Problems 3-4)
Use the scale 1 cm = 25 N. Draw force F with magnitude 125 N at 60° from the +x direction, and force G with magnitude 75 N at a bearing of S 30° W. Label the initial and terminal points of each, state the length of each arrow, and give the direction of G as an angle from the +x direction.
Vector u has initial point (-2, 1) and terminal point (7, 13). Draw u on a grid and find |u|. Then draw a vector equal to u that starts at the origin, and the vector -u that also starts at the origin. Give the terminal point of each.
Part 3: Using the Symbols (Problems 5-6)
A crate hangs at rest from a crane cable. Earth pulls the crate down with a force W of 2,000 N, and the cable pulls up with a force T. (a) Write the magnitude of W in two different ways. (b) The two forces balance. Write the relationship between T and W as a vector equation, and find |T|. (c) Explain why the equation T = W is false.
A student wrote three statements. For each one, explain the error and write a correct version: (i) v = 10 km/h (ii) |w| = 5 m/s east (iii) "The initial point of the vector KL is L."
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Scalar or Vector
Every quantity classified, with magnitude and direction named for vectors
Classification right but a direction or unit missing
Most quantities misclassified
Scale Drawings
Arrow lengths and angles correct, tail and head labeled
One length or angle off, or labels missing
Drawings not to scale or wrong direction
Notation
Vectors and magnitudes written with the right symbols throughout
One or two symbol errors
Vectors and magnitudes mixed up
Explanations
Clear reasons that use both magnitude and direction
Reason uses only one of the two ideas
No reason given
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. A bold letter is a vector; bars or an italic letter mean its magnitude. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which of these quantities is a vector?
Answer: C
A velocity has a size (3 m/s) and a direction (toward the dock), so it is a vector. Choices A, B and D are each described completely by one number with a unit. Choice B is a common trap: mass is a scalar, while weight, the force of gravity on that mass, is a vector.
Question 2 of 20 · Multiple Choice
Car X travels 60 km/h due north. Car Y travels 60 km/h due south. Which statement is true?
Answer: A
Speed is the magnitude only, 60 km/h for both. Velocity includes direction, and north is not south, so the velocities differ. Choice C treats velocity as if it were a scalar.
Question 3 of 20 · Multiple Choice
A pilot reports a velocity of 480 km/h on a heading of due west. What is the magnitude of this velocity?
Answer: D
The magnitude is only the size, 480 km/h. Choice B is the whole vector, magnitude and direction together, not the magnitude. Choices A and C are ways of writing the direction.
Question 4 of 20 · Multiple Choice
A drawing uses the scale 1 cm = 15 m/s. How long should the arrow for a velocity of 105 m/s be?
Answer: B
Divide the magnitude by the scale: 105 ÷ 15 = 7 cm. Choice A uses the scale number itself as the length. Choice D divides by 10 instead of by 15.
Question 5 of 20 · Multiple Choice
On a directed line segment, which point marks where the vector ends?
Answer: C
The terminal point, at the arrowhead, is where the vector ends. The initial point and the tail (choices A and B) are two names for the start of the arrow.
Question 6 of 20 · Multiple Choice
A vector has initial point (1, -2) and terminal point (6, 10). What is its magnitude?
Answer: A
The horizontal change is 5 and the vertical change is 12, so the length is √(5² + 12²) = √169 = 13. Choice B adds 5 and 12 instead of using the Pythagorean theorem. Choice C forgets the square root, and choice D subtracts the squares.
Question 7 of 20 · Multiple Choice
Vector k runs from A(0, 0) to B(3, 2). Which vector is equal to k?
Answer: D
Equal vectors have the same magnitude and direction: 3 right and 2 up. Choice D goes from (-2, 4) to (1, 6), which is 3 right and 2 up. Choice B has the same length but points the opposite way, so it is -k. Choice A goes 2 right and 3 up, a different direction.
Question 8 of 20 · Multiple Choice
A ship sails on a bearing of N 25° W. What is this direction as an angle measured counterclockwise from the +x (east) direction?
Answer: B
North is 90° from east. Turning 25° further toward west gives 90° + 25° = 115°. Choice A turns toward east instead (90° - 25°). Choice D measures 25° clockwise from east, which is a direction south of east.
Question 9 of 20 · Multiple Choice
Which symbol names the vector itself rather than its magnitude?
Answer: A
The bold letter names the vector, which carries both size and direction. The other three, |v|, ||v|| and italic v, all name the magnitude, a single nonnegative number.
Question 10 of 20 · Multiple Choice
A student draws vector m pointing to the left, 8 units long, and writes |m| = -8. Which statement describes the error?
Answer: C
A magnitude is a length and cannot be negative, so |m| = 8. The direction belongs to the vector m, not to its magnitude. Choice D attaches a direction to a magnitude, which mixes the two ideas.
Question 11 of 20 · Multiple Choice
Vectors a and b satisfy |a| = |b|. What can you conclude?
Answer: D
Equal magnitudes say nothing about direction. For example, 5 N north and 5 N east have equal magnitudes but are not equal vectors. Choices A and B would each need information about direction.
Question 12 of 20 · Multiple Choice
A forecast says the wind is "from the east at 20 km/h." In which direction is the air moving?
Answer: B
Winds are named for the direction they come from, so air coming from the east moves toward the west. Choice A reverses the direction. Choice D forgets that the report gives a direction as well as a speed, so it describes a vector.
Question 13 of 20 · Multiple Choice
Vector PQ goes from P to Q. Which statement about QP is true?
Answer: C
QP uses the same segment but starts at Q, so it has the same length and points the other way: QP = -PQ. Choice A ignores direction, and choice B gives a negative magnitude, which is impossible.
Question 14 of 20 · Multiple Choice
A diagram uses the scale 1 cm = 50 N. An arrow in it is 3.6 cm long. What force does it represent?
Answer: A
Multiply the length by the scale: 3.6 × 50 = 180 N. Choice B divides 50 by 3.6 instead of multiplying. Choice C adds the two numbers.
Question 15 of 20 · Short Answer
A student says, "Mass and weight are the same kind of quantity." Explain the difference using the words magnitude and direction. Use a 50 kg student as your example (use 9.8 m/s² for gravity).
Mass is a scalar: 50 kg has a magnitude and no direction. Weight is a force, so it is a vector: its magnitude is 50 × 9.8 = 490 N and its direction is straight down, toward the center of Earth.
Question 16 of 20 · Short Answer
Describe how to draw a velocity of 36 km/h at a bearing of S 50° E, using the scale 1 cm = 6 km/h. Also give the direction as an angle from the +x direction.
The arrow is 36 ÷ 6 = 6 cm long. Start by facing south, turn 50° toward east, and draw the arrow from the tail in that direction. South is 270° from +x, and turning toward east brings the angle back to 360°, so the direction is 270° + 50° = 320°.
Question 17 of 20 · Short Answer
Vector n has initial point (-3, 2) and terminal point (5, -4). Find |n| and describe its direction in words and as an angle from the +x direction.
The vector moves 8 units right and 6 units down, so |n| = √(8² + 6²) = 10. It points down and to the right, about 36.9° below the +x direction, which is an angle of about 323.1° measured counterclockwise from +x.
Question 18 of 20 · Short Answer
Vector u has magnitude 6, and vector q = -u. What is ||q||? Explain in one sentence how q and u are related.
||q|| = 6. The vector -u has the same magnitude as u and points in the opposite direction, so only the direction changes.
Question 19 of 20 · Short Answer
A student uses the scale 1 cm = 20 N and draws a 4.5 cm arrow to show a 50 N force. What is wrong? How long should the arrow be, and what force does the 4.5 cm arrow actually show?
At 1 cm = 20 N, a 50 N force needs 50 ÷ 20 = 2.5 cm. The 4.5 cm arrow shows 4.5 × 20 = 90 N, so the drawing almost doubles the force.
Question 20 of 20 · Short Answer
Two tugboats each pull a barge with a force of 5,000 N. Explain why the number 5,000 N alone is not enough to predict how the barge will move, and describe two different situations with sketches.
Force is a vector, so the effect depends on direction as well as magnitude. If both tugs pull the same way, the pulls work together and the barge speeds up in that direction. If they pull in opposite directions, the forces balance and a barge starting from rest does not start moving. The sketches should show two 5,000 N arrows of equal length, pointing the same way in one sketch and opposite ways in the other.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSN.VM.A.1 mean?
HSN.VM.A.1 asks students to recognize that some quantities have both a magnitude and a direction, to draw them as arrows (directed line segments), and to use the standard symbols for a vector and for its magnitude. It is the first standard in the Vector and Matrix Quantities domain, and it is marked (+), which means it is meant for students who go on to advanced courses.
Is HSN.VM.A.1 taught in Precalculus or Algebra 2?
It is usually taught in Precalculus. Some schools introduce vectors at the end of Algebra II or in a physics course, but in Common Core the (+) vector standards are part of the advanced mathematics that goes beyond the course sequence all students take.
What is the difference between a vector and a scalar?
A scalar is one number with a unit, such as 12 kg or 90 seconds. A vector needs a number and a direction, such as 12 m/s toward the northeast. A quick test: if you can ask "which way?" and the answer matters, the quantity is a vector.
Why are vectors written in bold, and how do students write them by hand?
Bold type separates the vector, which has a direction, from ordinary numbers. Textbooks print v, but bold is hard to write with a pencil, so students draw a small arrow over the letter. For a vector named by its endpoints, they draw an arrow over both letters, with the arrow pointing from the initial point to the terminal point.
What is the difference between |v|, ||v|| and italic v?
There is no difference in meaning: all three name the magnitude of the vector v. The double bars are common in later courses because single bars also mean the absolute value of a number. The italic letter is a shorthand used in physics, where v without bold is simply the speed. Teachers can pick one form for class work but should show students all three, because the standard lists them.
Is speed a vector?
No. Speed is a scalar: it tells how fast, but not which way. Velocity is the vector version. A car going 30 mph around a curve keeps the same speed while its velocity changes, because its direction changes.
Do two vectors have to start at the same point to be equal?
No. Two vectors are equal when they have the same magnitude and the same direction. Where the arrow is drawn does not matter, so a vector can be slid anywhere in the plane without changing it. Students who come from geometry sometimes expect equal vectors to share endpoints, like congruent segments that coincide.
How do you describe the direction of a vector?
Two common ways: an angle measured counterclockwise from the positive x-direction (as in trigonometry), or a compass bearing such as N 40° E, which starts at north and turns 40° toward east. Words such as "straight down" or "due west" also work when they are exact. Always say which reference is used, because 40° from east and 40° from north are different directions.
What mistakes do students make with vectors in this standard?
A frequent one is calling a quantity a vector without stating its direction. Others are giving a magnitude a sign or a direction, deciding that two vectors are equal because their lengths match, measuring a bearing from the wrong axis, and drawing an arrow without using the scale. Asking "how much and which way?" for every vector catches many of these.
How does HSN.VM.A.1 connect to later standards and to physics?
The next standard, HSN.VM.A.2, writes a vector in components by subtracting the coordinates of its initial point from those of its terminal point. HSN.VM.A.3 then solves velocity and force problems, and HSN.VM.B.4 adds vectors. In physics, force, velocity, acceleration and displacement are all vectors, so the arrow drawings from this standard become free-body diagrams and motion diagrams.
07
Related Standards
6 standards
These standards connect to HSN.VM.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.G.B.8Prerequisite
Use the Pythagorean theorem to find the distance between two points in a coordinate system
