1. Vectors and Geometry

Dot Product — Quiz

Test your understanding of dot product with 5 practice questions.

Practice Questions

Question 1

Which of the following is the correct definition of the dot product of two vectors $\mathbf{a}$ and $\mathbf{b}$ in terms of their components?

Question 2

What is the geometric interpretation of the dot product between two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$?

Question 3

If $\mathbf{a} = (3, -1, 2)$ and $\mathbf{b} = (-2, 4, 1)$, what is the value of $\mathbf{a} \cdot \mathbf{b}$?

Question 4

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

Question 5

Consider vectors $\mathbf{a} = (1, 2, 3)$ and $\mathbf{b} = (4, -2, 1)$. What is the angle $\theta$ between $\mathbf{a}$ and $\mathbf{b}$ to the nearest degree?