Question:
Find the position vector of the mid point of the vector joining the points \(P(2,3,4)\) and \(Q(4,1,-2)\).
Find the position vector of the mid point of the vector joining the points \(P(2,3,4)\) and \(Q(4,1,-2)\).
Updated On: Sep 19, 2023
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Solution and Explanation
The correct answer is: \(3\hat{i}+2\hat{j}+\hat{k}.\)
The position vector of mid point R of the vector joining points \(P(2,3,4)\) and \(Q(4,1,-2)\) is given by,
\(\vec{OR}=\frac{(2\hat{i}+3\hat{j}+4\hat{k})+(4\hat{i}+\hat{j}-2\hat{k})}{2}\)
\(=\frac{(2+4)\hat{i}+(3+1)\hat{j}+(4-2)\hat{k}}{2}\)
\(\implies \frac{6\hat{i}+4\hat{j}+2\hat{k}}{2}=3\hat{i}+2\hat{j}+\hat{k}.\)
The position vector of mid point R of the vector joining points \(P(2,3,4)\) and \(Q(4,1,-2)\) is given by,
\(\vec{OR}=\frac{(2\hat{i}+3\hat{j}+4\hat{k})+(4\hat{i}+\hat{j}-2\hat{k})}{2}\)
\(=\frac{(2+4)\hat{i}+(3+1)\hat{j}+(4-2)\hat{k}}{2}\)
\(\implies \frac{6\hat{i}+4\hat{j}+2\hat{k}}{2}=3\hat{i}+2\hat{j}+\hat{k}.\)
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