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
xyza

Find the magnitude |a| of the vector a = (−2, 0, −5).

a = (−2, 0, −5)
|a| =
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (7, 7, 6).

a = (7, 7, 6)
ûz =
3.Medium
xyzdFAB

A constant force F = (5, 5, −10) N acts on an object while it moves in a straight line from point A(1, 0, 4) to point B(1, −4, 0). Coordinates are in metres. Find the work W done by the force.

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

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

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

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

a = (0, −6, −2)b = (−1, 0, 1)
(a × b)y =
6.Hard
xyzab

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

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

Answer key

  1. 1. |a| = 5.385
  2. 2. ûz = 0.5183
  3. 3. W = 20 J
  4. 4. k = −8.5
  5. 5. (a × b)y = 2
  6. 6. (a × b)x = −10

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