Find the projection of the vector $\vec{a} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ on the vector $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$.

$\frac{5\sqrt{6}}{3}$

The correct answer is Option (1) → $\frac{5\sqrt{6}}{3}$ ##

The projection of the vector is:

$\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{(2 + 6 + 2)}{\sqrt{1^2 + 2^2 + 1^2}} = \frac{5\sqrt{6}}{3}$