If the position vector of A and B relative to O be \(\widehat{i}\, -4\widehat{j}+3\widehat{k}\) and \(-\widehat{i}\, +2\widehat{j}-\widehat{k}\) respectively, then the median through \(\overrightarrow O \) of ΔABC is:
The midpoint of \(A\) and \(B\), \(M\) is: \[ M = \left( \frac{1 - 1}{2}, \frac{-4 + 2}{2}, \frac{3 - 1}{2} \right) = (0, -1, 1) \] Hence, the vector \(\overrightarrow{OM}\) is: \[ \overrightarrow{OM} = -\hat{j} + \hat{k} \]
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