13. Inner Products and Orthogonality

Inner Products — Quiz

Test your understanding of inner products with 5 practice questions.

Practice Questions

Question 1

In $\mathbb{R}^2$, what is the standard inner product of $u=(1,2)$ and $v=(3,4)$?

Question 2

Which property of an inner product says that $\langle x,x\rangle \ge 0$ for every vector $x$, and that $\langle x,x\rangle = 0$ only when $x=0$?

Question 3

When two vectors have inner product $0$, they are called what?

Question 4

In $\mathbb{R}^3$, compute $\langle (2,-1,3),(0,4,5)\rangle$.

Question 5

Which property states that $\langle x,y\rangle = \langle y,x\rangle$ in a real inner product space?