6. Vectors and Matrices

Dot Product — Quiz

Test your understanding of dot product with 5 practice questions.

Practice Questions

Question 1

Given two vectors $\mathbf{a}$ and $\mathbf{b}$, if the angle $\theta$ between them is acute, what can be concluded about their dot product $\mathbf{a} \cdot \mathbf{b}$?

Question 2

What is the dot product of the vector $\mathbf{v} = \begin{pmatrix} 5 \\ 0 \end{pmatrix}$ and the vector $\mathbf{w} = \begin{pmatrix} 0 \\ 3 \end{pmatrix}$?

Question 3

Which of the following statements is true regarding the commutativity of the dot product?

Question 4

If the dot product of two vectors is negative, what type of angle exists between them?

Question 5

Given a vector $\mathbf{a} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, what is the magnitude of $\mathbf{a}$?