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
xy30°F = 290 N

A force of 290 N acts in the xy-plane at 30° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 290 Nθ = 30°
Fx = N
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (5, −2, −4).

a = (5, −2, −4)
ûz =
3.Medium
xyzab

Find the dot product a·b of a = (−7, −2, −3) and b = (1, 4, −7).

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

Find the dot product a·b of a = (−2, 4, −4) and b = (−5, −4, 6).

a = (−2, 4, −4)b = (−5, −4, 6)
a·b =
5.Hard
xyzab

For a = (4, 0, 3) and b = (3, 4, 0), find the y-component (a × b)y of the cross product a × b.

a = (4, 0, 3)b = (3, 4, 0)
(a × b)y =
6.Hard
xyzab

For a = (−3, 1, −4) and b = (2, 0, 6), find the x-component (a × b)x of the cross product a × b.

a = (−3, 1, −4)b = (2, 0, 6)
(a × b)x =

Answer key

  1. 1. Fx = 251.1 N
  2. 2. ûz = −0.5963
  3. 3. a·b = 6
  4. 4. a·b = −30
  5. 5. (a × b)y = 9
  6. 6. (a × b)x = 6

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