Question

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

Answer 1

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

Take A as the origin(0,0)

so $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $AC=5\hat{i}–2\hat{j}+4\hat{k}$ will become position vector.

So coordinate of B is $(3,0,4)$ and C is$(5,-2,4)$.

The mid point of BC can be easily found by midpoint formula of two points as $D(4,-1,4).$

so length of median through $A$ is $AD$$=\sqrt{(4-0{)}^2+(-1-0{)}^2+(4-0{)}^2}$

$=\sqrt{33}$