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
xy280°F = 290 N

A force of 290 N acts in the xy-plane at 280° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 290 Nθ = 280°
Fy = N
2.Easy
xya

Find the magnitude |a| of the vector a = (11, 8).

a = (11, 8)
|a| =
3.Medium
xyzab

Find the scalar projection compb a of a = (7, 5, 4) onto b = (−2, 4, 6), that is, the component of a in the direction of b.

a = (7, 5, 4)b = (−2, 4, 6)
compb a =
4.Medium
xyzdFAB

A constant force F = (−10, 25, 0) N acts on an object while it moves in a straight line from point A(1, 1, −4) to point B(4, 0, 0). Coordinates are in metres. Find the work W done by the force.

F = (−10, 25, 0) NA(1, 1, −4) mB(4, 0, 0) m
W = J
5.Hard
xyzab

For a = (−5, 4, 1) and b = (2, 4, 2), find the x-component (a × b)x of the cross product a × b.

a = (−5, 4, 1)b = (2, 4, 2)
(a × b)x =
6.Hard
xyzab

For a = (−2, −2, −5) and b = (−4, −2, −3), find the x-component (a × b)x of the cross product a × b.

a = (−2, −2, −5)b = (−4, −2, −3)
(a × b)x =

Answer key

  1. 1. Fy = −285.6 N
  2. 2. |a| = 13.6
  3. 3. compb a = 4.009
  4. 4. W = −55 J
  5. 5. (a × b)x = 4
  6. 6. (a × b)x = −4

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