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
xy265°F = 220 N

A force of 220 N acts in the xy-plane at 265° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 220 Nθ = 265°
Fx = N
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−4, 6, −2).

a = (−4, 6, −2)
ûy =
3.Medium
xyzab

Find the dot product a·b of a = (5, −1, 7) and b = (6, −3, −4).

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

Find the value of k for which the vectors a = (4, 5, −3) and b = (k, 1, −6) are perpendicular.

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

Find the area A of the parallelogram spanned by a = (0, −5, 2) and b = (4, −1, 3).

a = (0, −5, 2)b = (4, −1, 3)
A =
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (1, 1, −2) and b = (−4, 2, −1) and has a positive z-component. Find its y-component n̂y.

a = (1, 1, −2)b = (−4, 2, −1)n̂z > 0
n̂y =

Answer key

  1. 1. Fx = −19.17 N
  2. 2. ûy = 0.8018
  3. 3. a·b = 5
  4. 4. k = −5.75
  5. 5. A = 25.16
  6. 6. n̂y = 0.8018

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