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

The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, – 2) is given by,

$\overrightarrow{\mathrm{OR}}=\frac{(2 \hat{i}+3 \hat{j}+4 \hat{k})+(4 \hat{i}+\hat{j}-2 \hat{k})}{2}=\frac{(2+4) \hat{i}+(3+1) \hat{j}+(4-2) \hat{k}}{2}$

$=\frac{6 \hat{i}+4 \hat{j}+2 \hat{k}}{2}=3 \hat{i}+2 \hat{j}+\hat{k}$