## Problem on visually estimating the angle between vectors

Estimate the angle between the following pairs of vectors:
• ## Solution

Recall that
Lining up the bases of the vectors and connecting the vectors with the arc that directly connects them, we get:
We visually estimate that the angles between the pairs of vectors are (a) $\pi/4$, (b) $3\pi/4$, and (c) $\pi$.
We comment that in (c), the connecting arc could have been drawn on the other side of the vectors. In either case, the angle swept by it is $\pi$.