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 - Challenge Me

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

Two friends pull a sled: one with 10 N at 0°, the other with 10 N at 60°, angles from east. Ren adds them. To the nearest tenth, how large is the total?
A plane flies at 12 km/h at 30°, and the wind adds 5 km/h at 120°, angles from east. Tala adds them. To the nearest tenth, how large is the total?
Two ropes pull a boat: one with 20 N at 30°, the other with 15 N at 120°, angles from east. Zee adds them. To the nearest tenth, how large is the total?
Two kids pull a wagon: one with 6 N at 0°, the other with 10 N at 120°, angles from east. Esme adds them. To the nearest tenth, how large is the total?
A robot has two moves, u = ⟨1, 2⟩ and v = ⟨3, 1⟩. Kira wants a·u + b·v = ⟨7, 9⟩. Written as (a, b), what are the two numbers?
A game piece has two jumps, u = ⟨2, 1⟩ and v = ⟨1, 3⟩. Luz wants a·u + b·v = ⟨8, 9⟩. Written as (a, b), what are the two numbers?
A drone has two flight steps, u = ⟨1, -1⟩ and v = ⟨2, 3⟩. Milo wants a·u + b·v = ⟨9, 1⟩. Written as (a, b), what are the two numbers?
A crane has two arm moves, u = ⟨3, 2⟩ and v = ⟨-1, 1⟩. Noah wants a·u + b·v = ⟨2, 8⟩. Written as (a, b), what are the two numbers?
Two ropes pull a sled with F₁ = ⟨30, 40⟩ N and F₂ = ⟨50, -10⟩ N. Pia adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?
Two kids pull a wagon with F₁ = ⟨-20, 35⟩ N and F₂ = ⟨60, 15⟩ N. Ren adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?

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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