Vectors: dot & cross product worksheet with answers

Free printable Vectors: dot & cross product worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xy65°F = 260 N

A force of 260 N acts in the xy-plane at 65° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 260 Nθ = 65°
Fx = N
2.Easy
xy300°F = 310 N

A force of 310 N acts in the xy-plane at 300° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 310 Nθ = 300°
Fy = N
3.Medium
xyzab

Find the angle θ between the vectors a = (−5, 6, 2) and b = (−1, 0, 6), in degrees.

a = (−5, 6, 2)b = (−1, 0, 6)
θ = °
4.Medium
xyzab

Find the scalar projection compb a of a = (7, 2, 4) onto b = (1, −3, 5), that is, the component of a in the direction of b.

a = (7, 2, 4)b = (1, −3, 5)
compb a =
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (3, 4, 0) and b = (−3, 4, −2).

a = (3, 4, 0)b = (−3, 4, −2)
A =
6.Hard
xyzab

Find the area A of the parallelogram spanned by a = (3, −6, −2) and b = (0, 5, −5).

a = (3, −6, −2)b = (0, 5, −5)
A =

Answer key

  1. 1. Fx = 109.9 N
  2. 2. Fy = −268.5 N
  3. 3. θ = 69.72 °
  4. 4. compb a = 3.55
  5. 5. A = 26
  6. 6. A = 45.28

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