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