Question

The vector $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a $\Delta ABC$ where $A$ is the origin. The length of median through $A$ is

• A. $\sqrt{72}$
• B. $\sqrt{33}$
• C. $\sqrt{288}$
• D. $\sqrt{18}$

Answer 1

The correct option is B $\sqrt{33}$

Let $A$ be the origin.
$D$ is mid of $BC=(4,-1,4)$
So Length $AD=\sqrt{16+16+1}$
$=\sqrt{33}$