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
xy280°F = 30 N

A force of 30 N acts in the xy-plane at 280° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 30 Nθ = 280°
Fy = N
2.Easy
xy185°F = 320 N

A force of 320 N acts in the xy-plane at 185° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 320 Nθ = 185°
Fx = N
3.Medium
xyzab

Find the scalar projection compb a of a = (−5, −5, 0) onto b = (1, 5, −4), that is, the component of a in the direction of b.

a = (−5, −5, 0)b = (1, 5, −4)
compb a =
4.Medium
xyzdFAB

A constant force F = (−25, 20, 10) N acts on an object while it moves in a straight line from point A(5, 3, −3) to point B(−1, 2, −3). Coordinates are in metres. Find the work W done by the force.

F = (−25, 20, 10) NA(5, 3, −3) mB(−1, 2, −3) m
W = J
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (5, −6, −6) and b = (4, −1, −1).

a = (5, −6, −6)b = (4, −1, −1)
A =
6.Hard
xyzABC

Find the area A of the triangle with corners A(1, −3, 4), B(0, 4, −4) and C(−2, 0, −2). Coordinates are in metres.

A(1, −3, 4)B(0, 4, −4)C(−2, 0, −2)
A = m²

Answer key

  1. 1. Fy = −29.54 N
  2. 2. Fx = −318.8 N
  3. 3. compb a = −4.629
  4. 4. W = 130 J
  5. 5. A = 26.87
  6. 6. A = 15.59 m²

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