Question

If 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 $\Delta$ABC, then the length of the median through $A$ is

• A. $\sqrt{14}$
• B. $\sqrt{18}$
• C. $\sqrt{29}$
• D. $5$

Answer 1

Answer: (B)

$\sqrt{18}$

We know the median is $AD=\frac{\overrightarrow{a}+\overrightarrow{b}}{2}$

So the length of median is $\frac{|a+b|}{2}=\sqrt{18}$