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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xy215°F = 210 N

A force of 210 N acts in the xy-plane at 215° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 210 Nθ = 215°
Fx = N
2.Easy
xyza

Find the magnitude |a| of the vector a = (−8, −9, −8).

a = (−8, −9, −8)
|a| =
3.Medium
xyzab

Find the angle θ between the vectors a = (−3, 5, 0) and b = (5, −3, 5), in degrees.

a = (−3, 5, 0)b = (5, −3, 5)
θ = °
4.Medium
xyzdFAB

A constant force F = (25, −25, −30) N acts on an object while it moves in a straight line from point A(−4, −2, −4) to point B(5, −1, 0). Coordinates are in metres. Find the work W done by the force.

F = (25, −25, −30) NA(−4, −2, −4) mB(5, −1, 0) m
W = J
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (3, −6, 0) and b = (−2, −4, −4).

a = (3, −6, 0)b = (−2, −4, −4)
A =
6.Hard
xyzABC

Find the area A of the triangle with corners A(−3, 4, 4), B(−4, −4, 3) and C(3, 0, 0). Coordinates are in metres.

A(−3, 4, 4)B(−4, −4, 3)C(3, 0, 0)
A = m²

Answer key

  1. 1. Fx = −172 N
  2. 2. |a| = 14.46
  3. 3. θ = 132.1 °
  4. 4. W = 80 J
  5. 5. A = 36
  6. 6. A = 29.95 m²

Full step-by-step solutions: practise this topic on examproblems.com.