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
xy100°F = 90 N

A force of 90 N acts in the xy-plane at 100° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 90 Nθ = 100°
Fy = N
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (5, −1, −3).

a = (5, −1, −3)
ûz =
3.Medium
xyzab

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

a = (0, −5, −4)b = (−5, 1, −2)
compb a =
4.Medium
xyzab

Find the value of k for which the vectors a = (0, −6, −5) and b = (−5, −2, k) are perpendicular.

a = (0, −6, −5)b = (−5, −2, k)
k =
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (−3, −5, 1), b = (3, −3, −2) and c = (−2, −4, 3).

a = (−3, −5, 1)b = (3, −3, −2)c = (−2, −4, 3)
V =
6.Hard
xyzrFOA

A force F = (30, 50, −60) N acts at point A(−3, −3, 4). Coordinates are in metres. Find the magnitude |M| of the moment of the force about the origin O(0, 0, 0).

F = (30, 50, −60) NA(−3, −3, 4) mO(0, 0, 0) m
|M| = N·m

Answer key

  1. 1. Fy = 88.63 N
  2. 2. ûz = −0.5071
  3. 3. compb a = 0.5477
  4. 4. k = 2.4
  5. 5. V = 58
  6. 6. |M| = 87.18 N·m

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