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 triangle $ABC$. Then the length of the median through $A$ is

• A. $\sqrt{14}$
• B. $\sqrt{18}$
• C. $\sqrt{29}$
• D. none of these

Answer 1

The correct option is B $\sqrt{18}$

Let $A$ be the origin of reference so that the position vectors of

$B$ and $C$ are $-3\hat{i}+4\hat{k}$ and $5\hat{i}-2\hat{j}+4\hat{k}$ respectively

The position vector of mid point of $BC$ is $\hat{i}-\hat{j}+4\hat{k}$.

Thus the length of the median is $\sqrt{1+1+16}=\sqrt{18}$