Question

The vectors vector $AB=3\hat{i}+4\hat{k}$ and vector $AC=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of triangle $ABC.$The length of the median through $A$ is

• A. $7\sqrt{2}$
• B. $\sqrt{33}$
• C. $\sqrt{288}$
• D. $\sqrt{18}$

Answer 1

The correct option is B

$\sqrt{33}$

Explanation for the correct option:

A median of the triangle divides the opposite sides into two equal parts.

$$\begin{gathered} \therefore AB+AC=2AD \\ \Rightarrow AD=\frac{1}{2}\left[AB+AC\right] \\ \Rightarrow AD=\frac{1}{2}\left[8\hat{i}-2\hat{j}+8\hat{k}\right] \\ \Rightarrow \left|AD\right|=\sqrt{33} \end{gathered}$$

Hence the correct option is $\mathrm{Option}\left(\mathrm{B}\right)$