Question

if the vectors $\overline{AB}=3i+4k$ and $\overline{Ac}=5i+2j+4k$ are he sies of a $△ABC$ then the length of he medcian through A is

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

Answer 1

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

$\begin{array}{cc}\overrightarrow{AB}& =3i+4k\\ \overrightarrow{AC}& =5i+2j+4k\end{array}$

$\text{"- median through angle}$

$\overrightarrow{A}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}$

$=\frac{3i+4k+5i+2j+4k}{2}$

$\overrightarrow{AD}=4i+j+4k$

Now,

$\text{Length of}$

$\overrightarrow{AD}=\sqrt{(4{)}^2+1+(4{)}^2}$

$\overrightarrow{AD}=\sqrt{33}$

option. $\left(C\right)=\sqrt{33}$