Vectors $\vec{OA} = 2\hat{i} + 6\hat{k}$ and $\vec{OB} = 4\hat{i} - 2\hat{j} + 4\hat{k}$ are two sides of a $\Delta OAB$ where $O$ is the origin. Find the length of the median $\vec{OC}$.

$\sqrt{35}$ units

The correct answer is Option (3) → $\sqrt{35}$ units ##

When we draw a triangle $OAB$, since $\vec{OC}$ is the median, $C$ is the midpoint of $\vec{AB}$.

Hence, we can write:

$\vec{OC} = \frac{1}{2}(\vec{OA} + \vec{OB})$

$\vec{OC} = \frac{1}{2}(6\hat{i} - 2\hat{j} + 10\hat{k}) = 3\hat{i} - \hat{j} + 5\hat{k}$

The length of the median as $|\vec{OC}| = \sqrt{9 + 1 + 25}$

$= \sqrt{35} \text{ units.}$