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 = (−1, −4, 3).

a = (−1, −4, 3)
ûy =
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−3, 2, −7).

a = (−3, 2, −7)
ûy =
3.Medium
xyzab

Find the angle θ between the vectors a = (−2, −3, 3) and b = (5, −5, −2), in degrees.

a = (−2, −3, 3)b = (5, −5, −2)
θ = °
4.Medium
xyzab

Find the angle θ between the vectors a = (5, −2, 2) and b = (−4, 5, 3), in degrees.

a = (5, −2, 2)b = (−4, 5, 3)
θ = °
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (1, −1, 3) and b = (−3, 6, −4).

a = (1, −1, 3)b = (−3, 6, −4)
A =
6.Hard
xyzab

For a = (−6, 4, −5) and b = (5, 2, 3), find the y-component (a × b)y of the cross product a × b.

a = (−6, 4, −5)b = (5, 2, 3)
(a × b)y =

Answer key

  1. 1. ûy = −0.7845
  2. 2. ûy = 0.254
  3. 3. θ = 91.66 °
  4. 4. θ = 126.2 °
  5. 5. A = 15.17
  6. 6. (a × b)y = −7

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