Question

If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$, then the length of the median through $A$ is :

• A. $\sqrt{18}$
• B. $\sqrt{72}$
• C. $\sqrt{33}$
• D. $\sqrt{45}$

Answer 1

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

Median through any vertex divide the opposite sides into two parts


$\overrightarrow{AD}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}$
$=\frac{(3\hat{i}+4\hat{k})+(5\hat{i}-2\hat{j}+4\hat{k})}{2}$
$=4\hat{i}-\hat{j}+4\hat{k}$
Hence, $|\overrightarrow{AD}|=\sqrt{4^2+(-1{)}^2+4^2}$
$=\sqrt{33}$