More dot products:

Find all vectors orthogonal to $\langle 1, 3 \rangle.$

Compute the angle between the following vectors:

• $\langle 1,2,3 \rangle \cdot \langle 3,2,1 \rangle$
• $\langle 1,0,0 \rangle \cdot \langle 0, 1, 0 \rangle$
• $\langle 1,0,\cdots,0\rangle \cdot \langle 0, \cdots, 0, 1 \rangle$

Direction:

What is the angle between $\langle 1,-1,1 \rangle$ and each of the three standard unit vectors?

Note: the standard unit vectors in three dimensions are $\langle 1,0,0 \rangle$, $\langle 0,1,0 \rangle$, and $\langle 0,0,1 \rangle$.