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 = (8, 2, 2).

a = (8, 2, 2)
|a| =
2.Easy
xy95°F = 400 N

A force of 400 N acts in the xy-plane at 95° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 400 Nθ = 95°
Fx = N
3.Medium
xyzab

Find the value of k for which the vectors a = (1, −6, −3) and b = (k, 4, 0) are perpendicular.

a = (1, −6, −3)b = (k, 4, 0)
k =
4.Medium
xyzab

Find the dot product a·b of a = (7, −4, −4) and b = (−2, 0, 3).

a = (7, −4, −4)b = (−2, 0, 3)
a·b =
5.Hard
xyzABC

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

A(−3, −2, 1)B(3, 2, −2)C(2, 3, 2)
A = m²
6.Hard
xyzab

Find the area A of the parallelogram spanned by a = (0, 6, 3) and b = (−5, 1, −2).

a = (0, 6, 3)b = (−5, 1, −2)
A =

Answer key

  1. 1. |a| = 8.485
  2. 2. Fx = −34.86 N
  3. 3. k = 24
  4. 4. a·b = −26
  5. 5. A = 15.02 m²
  6. 6. A = 36.74

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