The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} \&…
The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} \& \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ are the sides of a triangle $\mathrm{ABC}$. The length of the median through $\mathrm{A}$ is
$\sqrt{288}$
$\sqrt{18}$
$\sqrt{72}$
$\sqrt{33}$
Solution
P.V of $\overrightarrow{\mathrm{AD}}=\frac{(3+5) \mathrm{i}+(0-2) \mathrm{j}+(4+4) \mathrm{k}}{2}$
$=4 \mathrm{i}-\mathrm{j}+4 \mathrm{k}$ or $|\overrightarrow{\mathrm{AD}}|=\sqrt{16+16+1}=\sqrt{33}$
