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 worksheet Practise 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

Two forces act at a point in the xy-plane: F₁ = 80 N at 145° and F₂ = 300 N at 65°, both measured anticlockwise from the positive x-axis. Find the direction φ of their resultant, measured anticlockwise from the positive x-axis (between 0° and 360°).

F₁ = 80 N, θ₁ = 145°F₂ = 300 N, θ₂ = 65°

φ = °

2.Easy

Find the z-component û_z of the unit vector û that points in the direction of a = (−7, 7, −1).

a = (−7, 7, −1)

û_z =

3.Medium

Find the value of k for which the vectors a = (−5, 6, 2) and b = (−2, k, −1) are perpendicular.

a = (−5, 6, 2)b = (−2, k, −1)

k =

4.Medium

Find the value of k for which the vectors a = (2, 6, −1) and b = (k, −4, 6) are perpendicular.

a = (2, 6, −1)b = (k, −4, 6)

k =

5.Hard

The unit vector n̂ is perpendicular to both a = (−4, −4, 0) and b = (−3, 3, 5) and has a positive z-component. Find its x-component n̂_x.

a = (−4, −4, 0)b = (−3, 3, 5)n̂_z > 0

n̂_x =

6.Hard

Find the area A of the parallelogram spanned by a = (2, 0, 3) and b = (1, −3, 2).

a = (2, 0, 3)b = (1, −3, 2)

A =

Answer key

1. φ = 79.09 °
2. û_z = −0.1005
3. k = −1.333
4. k = 15
5. n̂_x = 0.5392
6. A = 10.86

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