13. Inner Products and Orthogonality

Orthonormal Bases — Quiz

Test your understanding of orthonormal bases with 5 practice questions.

Practice Questions

Question 1

What does it mean for a set of vectors to be an orthonormal set?

Question 2

Which set is orthonormal in the plane?

Question 3

If $B=\{u_1,u_2,u_3\}$ is an orthonormal basis and $v=4u_1-u_2+2u_3$, what are the coordinates of $v$ relative to $B$?

Question 4

If $u_1$ and $u_2$ are an orthonormal basis for a subspace, what is the projection of a vector $v$ onto that subspace?

Question 5

If $u$ and $v$ are different vectors in an orthonormal set, what is $u \cdot v$?