Find the position vector of the mid point of the vector joining the points $P(2,3,4)\;{\rm{and}}\;Q(4,1,\; - 2)$ .

Mid-point of the vector joining the points $P(\vec a)$ and $Q(\vec b)$

$= \cfrac{{\vec a + \vec b}}{2}$
Here, $\vec a = 2\hat i + 3\hat j + 4\hat k$ and $\vec b = 4\hat i + \hat j - 2\hat k$

Required mid-point is $\left( {\cfrac{{(2\hat i + 3\hat j + 4\hat k) + (4\hat i + \hat j - 2\hat k)}}{2}} \right) = \cfrac{{6\hat i + 4\hat j + 2\hat k}}{2} = 3\hat i + 2\hat j + \hat k$