Problem on visually estimating the angle between vectors
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Estimate the angle between the following pairs of vectors:
Solution
Recall that
Definition of the angle between two vectors
The angle between two vectors is the angle swept by the arc that directly connects them, provided that the vectors share the same base.
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 $\pi$.
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