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
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (−6, −3, 1).

a = (−6, −3, 1)
ûz =
2.Easy
xy25°F = 50 N

A force of 50 N acts in the xy-plane at 25° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 50 Nθ = 25°
Fy = N
3.Medium
xyzab

Find the value of k for which the vectors a = (−3, 1, 3) and b = (2, −5, k) are perpendicular.

a = (−3, 1, 3)b = (2, −5, k)
k =
4.Medium
xyzdFAB

A constant force F = (10, 25, −15) N acts on an object while it moves in a straight line from point A(−1, 5, 5) to point B(−1, −3, −3). Coordinates are in metres. Find the work W done by the force.

F = (10, 25, −15) NA(−1, 5, 5) mB(−1, −3, −3) m
W = J
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (0, 4, −4) and b = (−4, 1, −6).

a = (0, 4, −4)b = (−4, 1, −6)
A =
6.Hard
xyzrFOA

A force F = (−40, 60, 20) N acts at point A(−4, 2, 2). Coordinates are in metres. Find the x-component Mx of the moment of the force about the origin O(0, 0, 0).

F = (−40, 60, 20) NA(−4, 2, 2) mO(0, 0, 0) m
Mx = N·m

Answer key

  1. 1. ûz = 0.1474
  2. 2. Fy = 21.13 N
  3. 3. k = 3.667
  4. 4. W = −80 J
  5. 5. A = 30.2
  6. 6. Mx = −80 N·m

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