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 - Challenge Me

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

Noah's kite string is a vector of length 12 units at 35° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?
Pia's rocket flight path is a vector of length 10 units at 58° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?
Tala's boat drift is a vector of length 10 units at 219° counterclockwise from the positive x-axis. To the nearest tenth, what is it in component form, as (run, rise)?
Zee's sailboat moves at 20 km/h on a bearing of N 41° E. To the nearest tenth, what is the velocity in component form, as (east, north), in km/h?
Ari's model plane flies at 30 mph on a bearing of N 65° W. To the nearest tenth, what is the velocity in component form, as (east, north), in mph?
Esme bikes at 24 km/h on a bearing of S 50° W. To the nearest tenth, what is the velocity in component form, as (east, north), in km/h?
Jun's robot slides straight from P(-2, 3) to Q(4, -1) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?
Kira's drone slides straight from P(5, -6) to Q(-1, 2) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?
Luz's scooter slides straight from P(-4, -7) to Q(2, 5) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?
Milo's boat slides straight from P(3, 8) to Q(-4, 1) on a map in kilometers. What is the length of vector PQ, as a simplified radical or whole number?

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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