1. Vectors and Geometry

Dot Product — Quiz

Test your understanding of dot product with 5 practice questions.

Practice Questions

Question 1

Given two vectors $\mathbf{a} = \langle 3, 4, 0 \rangle$ and $\mathbf{b} = \langle 1, -2, 5 \rangle$, what is their dot product $\mathbf{a} \cdot \mathbf{b}$?

Question 2

What is the geometric interpretation of the dot product of two vectors $\mathbf{u}$ and $\mathbf{v}$?

Question 3

If $\mathbf{u} = \langle 2, -1, 4 \rangle$ and $\mathbf{v} = \langle -3, 0, 2 \rangle$, what is the angle between $\mathbf{u}$ and $\mathbf{v}$? (Use $\cos^{-1}$ for inverse cosine and round to the nearest degree.)

Question 4

Which of the following statements is true about the dot product of two orthogonal (perpendicular) vectors $\mathbf{a}$ and $\mathbf{b}$?

Question 5

Let $\mathbf{a} = \langle 6, 8 \rangle$. Find the scalar projection of $\mathbf{a}$ onto $\mathbf{b} = \langle 3, 4 \rangle$.