Question

Find the position vector of the mid-point of the vector joining the points

\[P \left( 2 \hat{i} - 3\hat{ j} + 4 \hat{k} \right)\text{ and } Q \left( 4 \hat{i} + \hat{j} - 2 \hat{k} \right) .\]

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 =`\text{Position vector of P + Position vector of Q }/2`

\[= \frac{(2 \hat{i} - 3\hat{ j} + 4 \hat{k} ) +( 4 \hat{i} + \hat{j} - 2 \hat{k} )}{2}\]

\[ = \frac{6\hat{ i } - 2 \hat{j} + 2 \hat{k}}{2}\]

\[ = 3 \hat{i} - \hat{j} + \hat{k}\]