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Chapter 1

Q. 1.10

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

Step-by-Step

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.