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
xy260°F = 220 N

A force of 220 N acts in the xy-plane at 260° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 220 Nθ = 260°
Fy = N
2.Easy
xy215°F = 450 N

A force of 450 N acts in the xy-plane at 215° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 450 Nθ = 215°
Fy = N
3.Medium
xyzab

Find the scalar projection compb a of a = (−6, 7, −4) onto b = (5, 1, −3), that is, the component of a in the direction of b.

a = (−6, 7, −4)b = (5, 1, −3)
compb a =
4.Medium
xyzab

Find the angle θ between the vectors a = (−5, −4, 5) and b = (−6, −6, 0), in degrees.

a = (−5, −4, 5)b = (−6, −6, 0)
θ = °
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (4, −1, 5), b = (3, 3, 1) and c = (−4, 0, −5).

a = (4, −1, 5)b = (3, 3, 1)c = (−4, 0, −5)
V =
6.Hard
xyzab

Find the area A of the parallelogram spanned by a = (4, 5, −4) and b = (6, −6, −6).

a = (4, 5, −4)b = (6, −6, −6)
A =

Answer key

  1. 1. Fy = −216.7 N
  2. 2. Fy = −258.1 N
  3. 3. compb a = −1.859
  4. 4. θ = 38.43 °
  5. 5. V = 11
  6. 6. A = 76.37

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