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# Write the position vector of the mid-point of the vector joining the points P(2,3,4) and Q(4,1,-2).

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• Mid-point of two points is given by $\large\frac{\overrightarrow{OP}+\overrightarrow{OQ}}{2}$
Given :
Let $\overrightarrow{OP}=2\hat i+3\hat j+4\hat k$
Let $\overrightarrow{OQ}=4\hat i+\hat j-2\hat k$
Mid-point of two points is given by $\large\frac{\overrightarrow{OP}+\overrightarrow{OQ}}{2}$
$\Rightarrow \large\frac{2\hat i+3\hat j+4\hat k+4\hat i+\hat j-2\hat k}{2}$
$\Rightarrow \large\frac{ 6\hat i+4\hat j-2\hat k}{2}$
$\Rightarrow 3\hat i+2\hat j-\hat k$
answered Nov 11, 2013