Grade 11 · Math · Precalculus

11th grade Unit vectors, vector sums and combinations worksheet

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Unit vectors, vector sums and combinations

Grade 11 Math Worksheet - Building Confidence

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Esme draws u and then v tip to tail on the grid shown. What is the resultant u + v, written as (run, rise)?
Kira draws u and then v tip to tail on the grid shown. What is the resultant u + v, written as (run, rise)?
A boat's motor gives u = ⟨6, 0⟩ km/h and the river adds v = ⟨0, 8⟩. Noah works out the boat's speed. What is |u + v|, in km/h?
A drone's motors give u = ⟨0, 5⟩ m/s and a breeze adds v = ⟨12, 0⟩. Pia works out the drone's speed. What is |u + v|, in m/s?
Two ropes pull a cart with u = ⟨4, 3⟩ N and v = ⟨4, -3⟩. Ren works out the size of the total pull. What is |u + v|, in N?
Two friends tow a sled with u = ⟨8, 6⟩ N and v = ⟨-8, 6⟩. Tala works out the size of the total pull. What is |u + v|, in N?
Zee has v = ⟨3, 4⟩, whose length is 5. Written as (run, rise), what is the unit vector in the direction of v?
Esme has v = ⟨-5, 12⟩, whose length is 13. Written as (run, rise), what is the unit vector in the direction of v?
Kira has v = ⟨8, -6⟩, whose length is 10. Written as (run, rise), what is the unit vector in the direction of v?
Luz has v = ⟨-15, -8⟩, whose length is 17. Written as (run, rise), what is the unit vector in the direction of v?

Unit vectors, vector sums and combinations. Every version has 10 questions, and the answer key prints on the second page.

I can draw u + v tip to tail or as a parallelogram diagonal and read it as (run, rise).
I can find the length and direction of a sum, a unit vector, and a vector of any length in a given direction.
I can combine vectors, add vectors given by length and angle, and find the numbers a and b that build one vector from two others.

Standard: N-VM.A.1 (+), N-VM.A.2 (+), N-VM.A.3 (+), N-VM.B.4 (+), N-VM.B.5 (+)

resultant: The single arrow that does the same as two arrows one after the other.

unit vector: An arrow of length 1 pointing the same way.

i, j: The unit arrows along x and along y.

linear combination: a·u + b·v: copies of u and v added together.

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

Gave the point where the arrows end instead of the slide from start to end. A vector says how far across and up, not where.

Subtracted where the vectors were added. Adding is one slide after another; walk the two slides on a grid together.

Read the parallelogram's other diagonal, which is v − u. The sum starts at the shared tail.

What is the most common mistake with unit vectors, vector sums and combinations?

Gave the point where the arrows end instead of the slide from start to end. A vector says how far across and up, not where.

Are these 11th 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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