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 y-component ûy of the unit vector û that points in the direction of a = (−3, −4, −7).

a = (−3, −4, −7)
ûy =
2.Easy
xy95°F = 170 N

A force of 170 N acts in the xy-plane at 95° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 170 Nθ = 95°
Fx = N
3.Medium
xyzab

Find the value of k for which the vectors a = (2, 3, 5) and b = (6, −2, k) are perpendicular.

a = (2, 3, 5)b = (6, −2, k)
k =
4.Medium
xyzab

Find the dot product a·b of a = (1, 5, −5) and b = (0, −7, −5).

a = (1, 5, −5)b = (0, −7, −5)
a·b =
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (−2, −4, −3), b = (−2, −4, 3) and c = (1, 5, 5).

a = (−2, −4, −3)b = (−2, −4, 3)c = (1, 5, 5)
V =
6.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (0, 1, −5), b = (2, −2, 2) and c = (4, −1, 3).

a = (0, 1, −5)b = (2, −2, 2)c = (4, −1, 3)
V =

Answer key

  1. 1. ûy = −0.465
  2. 2. Fx = −14.82 N
  3. 3. k = −1.2
  4. 4. a·b = −10
  5. 5. V = 36
  6. 6. V = 28

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