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## Q. 1.10

Find the vector v whose direction is 5π/4 and whose magnitude is 7.

## Verified Solution

A unit vector $\mathbf{u}$ with direction $5 \pi / 4$ is given by

$\mathbf{u}=\left(\cos \frac{5 \pi}{4}\right) \mathbf{i}+\left(\sin \frac{5 \pi}{4}\right) \mathbf{j}=-\frac{1}{\sqrt{2}} \mathbf{i}-\frac{1}{\sqrt{2}} \mathbf{j}$

Then $\mathbf{v}=7 \mathbf{u}=-(7 / \sqrt{2}) \mathbf{i}-(7 / \sqrt{2}) \mathbf{j}$. This vector is sketched in Figure 16a. In Figure $16 \mathrm{~b}$ we have translated $\mathbf{v}$ so that it points toward the origin. This representation of $\mathbf{v}$ will be useful in Section 1.3.