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Q. The unit vector along $\hat{i}+\hat{j}$ is

Motion in a Plane

Solution:

$\hat{R}=\frac{\vec{R}}{|R|}=\frac{\hat{i}+\hat{j}}{\sqrt{1^{2}+1^{2}}}$
$=\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}$