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 z-component ûz of the unit vector û that points in the direction of a = (6, −6, 1).

a = (6, −6, 1)
ûz =
2.Easy
xyza

Find the magnitude |a| of the vector a = (9, −7, 0).

a = (9, −7, 0)
|a| =
3.Medium
xyzab

Find the value of k for which the vectors a = (6, −2, −6) and b = (1, k, −5) are perpendicular.

a = (6, −2, −6)b = (1, k, −5)
k =
4.Medium
xyzdFAB

A constant force F = (−15, −20, −5) N acts on an object while it moves in a straight line from point A(2, −4, −3) to point B(5, −3, −2). Coordinates are in metres. Find the work W done by the force.

F = (−15, −20, −5) NA(2, −4, −3) mB(5, −3, −2) m
W = J
5.Hard
xyzabc

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

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

A force F = (−10, −30, 20) N acts at point A(3, −2, −2). Coordinates are in metres. Find the y-component My of the moment of the force about point O(0, 0, 2).

F = (−10, −30, 20) NA(3, −2, −2) mO(0, 0, 2) m
My = N·m

Answer key

  1. 1. ûz = 0.117
  2. 2. |a| = 11.4
  3. 3. k = 18
  4. 4. W = −70 J
  5. 5. V = 101
  6. 6. My = −20 N·m

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