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
xy55°F = 330 N

A force of 330 N acts in the xy-plane at 55° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 330 Nθ = 55°
Fx = N
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−4, 4, 7).

a = (−4, 4, 7)
ûy =
3.Medium
xyzab

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

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

Find the scalar projection compb a of a = (6, −1, 5) onto b = (−4, 0, 2), that is, the component of a in the direction of b.

a = (6, −1, 5)b = (−4, 0, 2)
compb a =
5.Hard
xyzabc

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

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

For a = (6, 6, 5) and b = (3, 3, −6), find the y-component (a × b)y of the cross product a × b.

a = (6, 6, 5)b = (3, 3, −6)
(a × b)y =

Answer key

  1. 1. Fx = 189.3 N
  2. 2. ûy = 0.4444
  3. 3. compb a = 3.015
  4. 4. compb a = −3.13
  5. 5. V = 76
  6. 6. (a × b)y = 51

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