Grade 11 · Math · Precalculus

11th grade Vectors in three dimensions worksheet

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Vectors in three dimensions

Grade 11 Math Worksheet

NameDate

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

Luz has u = ⟨-1, 6, 0⟩ and v = ⟨3, 2, -4⟩. Written as (x, y, z), what is u − v?
Milo has u = ⟨7, 1, -3⟩ and v = ⟨-2, 5, -6⟩. Written as (x, y, z), what is u − v?
Noah has u = ⟨0, -4, 8⟩ and v = ⟨5, -1, 3⟩. Written as (x, y, z), what is u − v?
Pia needs the unit vector in the direction of v = ⟨2, -3, 6⟩. Written as (x, y, z) with fractions, what is it?
Ren needs the unit vector in the direction of v = ⟨-4, 4, 7⟩. Written as (x, y, z) with fractions, what is it?
Tala needs the unit vector in the direction of v = ⟨1, -8, -4⟩. Written as (x, y, z) with fractions, what is it?
Zee needs the unit vector in the direction of v = ⟨-6, 2, -9⟩. Written as (x, y, z) with fractions, what is it?
A zip line runs from post (2, 0, 5) to (4, 4, 9), in meters. Jun finds the straight-line distance. How many meters is it?
A robot arm moves a block from (-1, 3, 0) to (7, -1, 1), in meters. Kira finds the straight-line distance. How many meters is it?
A balloon rises from (0, -2, 4) to (9, 4, 6), in meters. Luz finds the straight-line distance. How many meters is it?

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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