Grade 11 · Math · Precalculus

11th grade Vectors in three dimensions worksheet

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Vectors in three dimensions

Grade 11 Math Worksheet - Building Confidence

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

A drone flies from its pad along v = ⟨2, 3, 6⟩ m, with x east, y north and z up. Esme finds how far that is. What is |v|, in m?
A kite's string runs from the spool along v = ⟨1, 4, -8⟩ m, with x east, y north and z up. Jun finds how far that is. What is |v|, in m?
A crane moves a load along v = ⟨-2, 6, 9⟩ m, with x east, y north and z up. Kira finds how far that is. What is |v|, in m?
A balloon drifts from the field along v = ⟨2, -10, 11⟩ m, with x east, y north and z up. Luz finds how far that is. What is |v|, in m?
Milo draws an arrow from P(1, 2, -1) to Q(4, -2, 3). Written as (x, y, z), what is the component form of the arrow from P to Q?
Noah draws an arrow from P(0, 5, 2) to Q(3, 1, 7). Written as (x, y, z), what is the component form of the arrow from P to Q?
Pia draws an arrow from P(-2, 4, 6) to Q(1, 4, -3). Written as (x, y, z), what is the component form of the arrow from P to Q?
A robot repeats the move v = ⟨2, -1, 4⟩, scaled by 3. Tala writes 3v. Written as (x, y, z), what is 3v?
A game piece repeats the jump v = ⟨-3, 0, 2⟩, scaled by 4. Esme writes 4v. Written as (x, y, z), what is 4v?
A crane reverses the move v = ⟨2, -2, 5⟩, scaled by -3. Jun writes -3v. Written as (x, y, z), what is -3v?

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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