Write a unit vector in the direction of a = 2i - 6j + 3k. - Vidyadip

Question

Write a unit vector in the direction of $\overrightarrow{a} = 2\hat{i} - 6\hat{j} + 3\hat{k}.$

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Answer

$\frac{2}{7} \hat{i} - \frac{6}{7} \hat{j} + \frac{3}{7} \hat{k}$Unit vector in the direction $\overrightarrow{a} = \frac{\overrightarrow{a}}{|\overrightarrow{b}|} = \hat{a}$
$\Rightarrow \hat{a} = \frac{2\hat{i}- 6\hat{j} + 3\hat{k}}{\sqrt{4 + 36 + 9}}$
$\Rightarrow \hat{a} = \frac{2}{7} \hat{i} - \frac{6}{7} \hat{j} + \frac{3}{7} \hat{k}$

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