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Question
Find the position vector of the mid-point of the vector joining the points
Solution
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`
\[= \frac{(2 \hat{i} - 3\hat{ j} + 4 \hat{k} ) +( 4 \hat{i} + \hat{j} - 2 \hat{k} )}{2}\]
\[ = \frac{6\hat{ i } - 2 \hat{j} + 2 \hat{k}}{2}\]
\[ = 3 \hat{i} - \hat{j} + \hat{k}\]
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