Question

Find the position vector of the mid point of the vector joining the points $P(2,3,4)$ and $Q(4,1,-2)$.

Answer 1

The correct answer is: $3\hat{i}+2\hat{j}+\hat{k}.$
The position vector of mid point R of the vector joining points $P(2,3,4)$ and $Q(4,1,-2)$ is given by,
$\vec{OR}=\frac{(2\hat{i}+3\hat{j}+4\hat{k})+(4\hat{i}+\hat{j}-2\hat{k})}{2}$
$=\frac{(2+4)\hat{i}+(3+1)\hat{j}+(4-2)\hat{k}}{2}$
$\implies \frac{6\hat{i}+4\hat{j}+2\hat{k}}{2}=3\hat{i}+2\hat{j}+\hat{k}.$