Grade 10 · Math · Geometry

10th grade Vectors: magnitude, direction and component form worksheet

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Vectors: magnitude, direction and component form

Grade 10 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

A toy robot rolls from P to Q on Milo's grid mat. What is vector PQ in component form, written as (run, rise)?
On Noah's map game, a token slides from P to Q. What is vector PQ in component form, written as (run, rise)?
Tala's paper rocket glides from P to Q across a grid poster. What is vector PQ in component form, written as (run, rise)?
Zee's drone makes the slide v = ⟨-6, 8⟩ in meters. What is the length (magnitude) of v, in meters?
Ari's kite makes the slide v = ⟨-5, 12⟩ in meters. What is the length (magnitude) of v, in meters?
Bo's boat makes the slide v = ⟨8, -15⟩ in meters. What is the length (magnitude) of v, in meters?
Esme's robot makes the slide v = ⟨-9, -12⟩ in meters. What is the length (magnitude) of v, in meters?
8.
Jun moves a game piece by the vector ⟨-3, 4⟩. Which slide is that?
- 3 units left and 4 units down
- 3 units left and 4 units up
- 4 units left and 3 units up
- 3 units right and 4 units up
9.
Kira moves a game piece by the vector ⟨5, -2⟩. Which slide is that?
- 5 units left and 2 units down
- 2 units right and 5 units down
- 5 units right and 2 units down
- 5 units right and 2 units up
10.
Luz moves a game piece by the vector ⟨-6, -1⟩. Which slide is that?
- 6 units left and 1 unit down
- 6 units left and 1 unit up
- 6 units right and 1 unit up
- 1 unit left and 6 units down

10th grade Vectors: magnitude, direction and component form worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Vectors: length, direction and component form. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write a vector as (run, rise) from its tail and head.
I can find a vector's length and its direction angle.
I can split a length and an angle, or a speed on a bearing, into components.

Standard: N-VM.A.1 (+), N-VM.A.2 (+), N-VM.A.3 (+)

Words to know

vector: A slide with a size and a direction, drawn as an arrow.

tail, head: Where the arrow starts and where it ends.

component form: The slide written as (run, rise): across first, then up or down.

direction angle: The turn from the positive x-axis to the arrow, counterclockwise.

bearing: A direction measured from north or south toward east or west, like N 41° E.

Common mistakes

Subtracted the head's coordinates from the tail's, so the arrow points backward. A vector is head minus tail. Trace the arrow from start to end together.

Wrote the up-down part first. A vector is written (across, up-down), like a point. Say "run, then rise" together.

Dropped a minus sign, so a slide left or down became right or up. Point the arrow on a grid together and check its direction.

Questions parents ask

What is the most common mistake with vectors: magnitude, direction and component form?

Subtracted the head's coordinates from the tail's, so the arrow points backward. A vector is head minus tail. Trace the arrow from start to end together.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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