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 = (−1, −7, −9).

a = (−1, −7, −9)
|a| =
2.Easy
xyza

Find the x-component ûx of the unit vector û that points in the direction of a = (2, −6, −3).

a = (2, −6, −3)
ûx =
3.Medium
xyzab

Find the value of k for which the vectors a = (6, 4, −5) and b = (k, −2, 1) are perpendicular.

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

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

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

For a = (6, −2, 4) and b = (−4, −6, −1), find the z-component (a × b)z of the cross product a × b.

a = (6, −2, 4)b = (−4, −6, −1)
(a × b)z =
6.Hard
xyzABC

Find the area A of the triangle with corners A(−1, 1, 3), B(4, 2, −3) and C(3, −2, 1). Coordinates are in metres.

A(−1, 1, 3)B(4, 2, −3)C(3, −2, 1)
A = m²

Answer key

  1. 1. |a| = 11.45
  2. 2. ûx = 0.2857
  3. 3. k = 2.167
  4. 4. k = 6
  5. 5. (a × b)z = −44
  6. 6. A = 15.47 m²

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