The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ and…
The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{k}}+4 \hat{\mathrm{k}}$ are the sies of a triangle $\mathrm{ABC}$. The length of the median through $\mathrm{A}$ is
$\sqrt{33}$ unit
$\sqrt{288}$ unit
$\sqrt{18}$ unit
$\sqrt{72}$ unit
Solution
Let $\mathrm{A}$ be the origin.
Then $\mathrm{B}=(3,0,4)$ and $\mathrm{C}=(5,-1,4)$
Mid point of $\mathrm{BC}=\left(\frac{3+5}{2}, \frac{0-2}{2}, \frac{4+4}{2}\right)$ i.e. $(4,-1,4)$
$\therefore$ Length of medium $=\sqrt{(4)^2+(-1)^2+(4)^2}=\sqrt{33}$