Question

Find the position vector of the mid-point of the vector joining the points $P\left(2\hat{i}-3\hat{j}+4\hat{k}\right)\mathrm{and}Q\left(4\hat{i}+\hat{j}-2\hat{k}\right).$

Answer 1

Given: $P\left(2\hat{i}-3\hat{j}+4\hat{k}\right)$ and $Q\left(4\hat{i}+\hat{j}-2k\right)$
The position vector of the midpoint of the vector
joining these points =$\frac{\mathrm{Position}\mathrm{vector}\mathrm{of}P+\mathrm{Position}\mathrm{vector}\mathrm{of}Q}{2}$
$$\begin{gathered} =\frac{(2\hat{i}-3\hat{j}+4\hat{k})+(4\hat{i}+\hat{j}-2\hat{k})}{2} \\ =\frac{6\hat{i}-2\hat{j}+2\hat{k}}{2} \\ =3\hat{i}-\hat{j}+\hat{k} \end{gathered}$$