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 = (−7, 5, 1).

a = (−7, 5, 1)
|a| =
2.Easy
xyza

Find the x-component ûx of the unit vector û that points in the direction of a = (−4, −4, 6).

a = (−4, −4, 6)
ûx =
3.Medium
xyzab

Find the value of k for which the vectors a = (−5, 6, 3) and b = (−6, k, −3) are perpendicular.

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

Find the value of k for which the vectors a = (1, 6, −6) and b = (−4, 1, k) are perpendicular.

a = (1, 6, −6)b = (−4, 1, k)
k =
5.Hard
xyzab

For a = (5, −1, −6) and b = (−4, 6, −4), find the z-component (a × b)z of the cross product a × b.

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

For a = (−1, −5, 1) and b = (−4, 2, 3), find the y-component (a × b)y of the cross product a × b.

a = (−1, −5, 1)b = (−4, 2, 3)
(a × b)y =

Answer key

  1. 1. |a| = 8.66
  2. 2. ûx = −0.4851
  3. 3. k = −3.5
  4. 4. k = 0.3333
  5. 5. (a × b)z = 26
  6. 6. (a × b)y = −1

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