Find unit vector in the direction of vector $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$.

$\frac{1}{\sqrt{14}}(2\hat{i} + 3\hat{j} + \hat{k})$

The correct answer is Option (2) → $\frac{1}{\sqrt{14}}(2\hat{i} + 3\hat{j} + \hat{k})$ ##

The unit vector in the direction of a vector $\vec{a}$ is given by $\hat{a} = \frac{1}{|\vec{a}|}\vec{a}$.

Now $|\vec{a}| = \sqrt{2^2 + 3^2 + 1^2} = \sqrt{14}$

Therefore $\hat{a} = \frac{1}{\sqrt{14}}(2\hat{i} + 3\hat{j} + \hat{k}) = \frac{2}{\sqrt{14}}\hat{i} + \frac{3}{\sqrt{14}}\hat{j} + \frac{1}{\sqrt{14}}\hat{k}$