Question

If the vectors $AB=3\hat{i}+4\hat{k}$, and $AC=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a $△ABC$, then the length of the median through $A$ is

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

Answer 1

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

Let $D$ be the midpoint of $BC$. Then
$AD=\frac{AB+AC}{2}$
$\Rightarrow AD=\frac{(3\hat{i}+4\hat{k})+(5\hat{i}-2\hat{j}+4\hat{k})}{2}=4\hat{i}+\hat{j}+4\hat{k}$
$\Rightarrow \left|AD\right|=\sqrt{16+1‘+16}=\sqrt{33}$