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

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A kayak paddles with u = ⟨3, 1⟩ and is pushed by v = ⟨-5, 2⟩. Milo plots u + v. To the nearest tenth of a degree, what is its direction angle?
A robot rolls with u = ⟨4, -1⟩ and is pushed by v = ⟨-6, -3⟩. Noah plots u + v. To the nearest tenth of a degree, what is its direction angle?
A toy boat drifts with u = ⟨-1, 4⟩ and is pushed by v = ⟨-3, -1⟩. Ren plots u + v. To the nearest tenth of a degree, what is its direction angle?
Tala has u = 2i − j and v = -4i + 3j. In the form ai + bj, what is 3u − 2v?
Zee has u = i + 5j and v = 3i − 2j. In the form ai + bj, what is 4u − 3v?
Esme has u = -3i + 2j and v = 2i + 6j. In the form ai + bj, what is 2u − 5v?
A tow rope pulls a cart with a force of 15 N in the direction of d = ⟨3, 4⟩. Luz writes it as a vector. As (run, rise), what is it?
A kite string pulls with a force of 26 N in the direction of d = ⟨5, 12⟩. Milo writes it as a vector. As (run, rise), what is it?
A robot is told to roll 5 m in the direction of d = ⟨-8, 6⟩. Noah writes it as a vector. As (run, rise), what is it?
A sled is pulled with a force of 39 N in the direction of d = ⟨-12, -5⟩. Pia writes it as a vector. As (run, rise), what is it?

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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