Find the position vector of the mid point of the vector joining the points $$P (2, 3, 4)$$ and $$Q (4, 1, 2)$$.
The position vector of mid-point $$R$$ of the vector joining points $$P (2, 3, 4)$$ and $$Q (4, 1, -2)$$ is given by,
$$\vec {OR}=\dfrac {(2\hat {i}+3\hat {j}+4\hat {k})+(4\hat {i}+\hat {j}-2\hat {k})}{2}=\dfrac {(2+4)\hat {i}+(3+1)\hat {j}+(4-2)\hat {k}}{2}$$
$$=\dfrac {6\hat {i}+4\hat {j}+2\hat {k}}{2}=3\hat {i}+2\hat {j}+\hat {k}$$
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$$ABCD$$ is a quadrilateral, $$E$$ is the point of intersection of the line joining the midpoints of the opposite sides. If $$O$$ is any point and $$\vec{OA} + \vec{OB} + \vec{OC} + \vec{OD} = \vec{x OE},$$ then $$x$$ is equal to
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