1. Vectors and Geometry

Cross Product — Quiz

Test your understanding of cross product with 5 practice questions.

Practice Questions

Question 1

What is the definition of the cross product of two vectors $\mathbf{a}$ and $\mathbf{b}$ in three-dimensional space?

Question 2

Which of the following is the correct formula for the cross product of two vectors $\mathbf{a} = \langle a_1, a_2, a_3 \rangle$ and $\mathbf{b} = \langle b_1, b_2, b_3 \rangle$?

Question 3

If $\mathbf{u} = \langle 1, 0, 0 \rangle$ and $\mathbf{v} = \langle 0, 1, 0 \rangle$, what is $\mathbf{u} \times \mathbf{v}$?

Question 4

What is the magnitude of the cross product $\mathbf{a} \times \mathbf{b}$ if $\mathbf{a}$ and $\mathbf{b}$ are vectors with magnitudes $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 4$, and the angle between them is $\frac{\pi}{2}$?

Question 5

If $\mathbf{a} = \langle 2, -1, 3 \rangle$ and $\mathbf{b} = \langle -3, 4, 1 \rangle$, what is $\mathbf{a} \times \mathbf{b}$?