Grade 11 · Math · Precalculus

11th grade Vectors in three dimensions worksheet

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Vectors in three dimensions

Grade 11 Math Worksheet - Challenge Me

NameDate

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

Noah has u = ⟨-3, 0, 4⟩ and v = ⟨1, 2, 2⟩. Written as (x, y, z), what is 3u − 2v?
Ren has u = ⟨0, 3, -2⟩ and v = ⟨5, -1, 1⟩. Written as (x, y, z), what is 2u − 5v?
A drone climbs 21 m in the direction of d = ⟨2, 3, 6⟩. Tala writes the move as a vector. Written as (x, y, z), what is it?
A diver's camera sinks 27 m in the direction of d = ⟨1, -4, 8⟩. Zee writes the move as a vector. Written as (x, y, z), what is it?
A crane swings a load 22 m in the direction of d = ⟨-2, 6, 9⟩. Esme writes the move as a vector. Written as (x, y, z), what is it?
A ball rolls down a ramp 18 cm in the direction of d = ⟨4, 4, -7⟩. Jun writes the move as a vector. Written as (x, y, z), what is it?
Kira knows v = ⟨2, y, 6⟩ has length 7 and y is positive. What is y?
Luz knows v = ⟨1, y, 8⟩ has length 9 and y is positive. What is y?
Milo knows v = ⟨6, y, 9⟩ has length 11 and y is positive. What is y?
Noah knows v = ⟨10, y, 11⟩ has length 15 and y is positive. What is y?

Vectors in three dimensions. Every version has 10 questions, and the answer key prints on the second page.

I can find the length of ⟨x, y, z⟩ and the arrow from one point to another.
I can add, subtract and scale 3-D vectors and find a unit vector.
I can make a vector of a given length, combine vectors, and find a missing part from the length.

Standard: N-VM.A.1 (+), N-VM.A.2 (+), N-VM.B.4 (+), N-VM.B.5 (+) (extended to three dimensions)

3-D vector ⟨x, y, z⟩: A slide: x east, y north, z up.

component form: A vector written as its three parts.

magnitude: The length of the arrow: √(x² + y² + z²).

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

Added the three parts to get the length. The length is the long diagonal of a box: square the parts, add, and take the square root.

Stopped at a square and skipped the square root.

Subtracted in the wrong order. An arrow from P to Q is Q − P, head minus tail; u − v starts with u.

Ask: is this the length, or the length squared?

What is the most common mistake with vectors in three dimensions?

Added the three parts to get the length. The length is the long diagonal of a box: square the parts, add, and take the square root.

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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