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. $\sqrt{14}$
• B. $\sqrt{18}$
• C. $\sqrt{29}$
• D. $4$

Answer 1

Answer: (B)

$\overrightarrow{ AD }=\frac{(-3+5) \hat{i}+(0-2) \hat{j}+(4+4) \hat{k}}{2}$
$=\frac{2 \hat{i}-2 \hat{j}+8 \hat{k}}{2}=\hat{i}-\hat{j}+4 \hat{k}$
$\therefore $ Length of median $=| AD |=\sqrt{18}$