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 x-component ûx of the unit vector û that points in the direction of a = (1, 2, 5).

a = (1, 2, 5)
ûx =
2.Easy
xyza

Find the magnitude |a| of the vector a = (3, −7, 4).

a = (3, −7, 4)
|a| =
3.Medium
xyzab

Find the dot product a·b of a = (5, 7, 6) and b = (−2, −2, −4).

a = (5, 7, 6)b = (−2, −2, −4)
a·b =
4.Medium
xyzab

Find the scalar projection compb a of a = (0, −3, 1) onto b = (−5, 3, 0), that is, the component of a in the direction of b.

a = (0, −3, 1)b = (−5, 3, 0)
compb a =
5.Hard
xyzab

For a = (6, 4, 1) and b = (2, 0, −4), find the y-component (a × b)y of the cross product a × b.

a = (6, 4, 1)b = (2, 0, −4)
(a × b)y =
6.Hard
xyzabc

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

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

Answer key

  1. 1. ûx = 0.1826
  2. 2. |a| = 8.602
  3. 3. a·b = −48
  4. 4. compb a = −1.543
  5. 5. (a × b)y = 26
  6. 6. V = 19

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