 Hi friends, I am Poojwa and today we will discuss the following question. Find the position vector of the midpoint of the vector joining the points P2,3,4 and Q4,1,-2. Let P and Q be the two points represented by the position vectors, vector OP and vector OQ respectively with respect to the origin O and let R be the point which divides PQ internally in the ratio m is to n. Then the position vector of the point R is given by vector OR is equal to m into vector B plus n into vector A upon m plus n. Now if R is the midpoint of PQ then we have m is equal to n and this is when R is the midpoint of PQ. Then the position vector of the point R is given by vector OR is equal to vector A plus vector B upon 2 because m becomes equal to n which is equal to 1. So we get vector OR is equal to vector A plus vector B upon 2. So this is the key idea behind our question. Let us begin with the solution now. Now let R of x,y,z be the midpoint of PQ. Now since R divides PQ in the ratio 1 is to 1 therefore we have x is equal to 2 plus 4 upon 1 plus 1, y is equal to 3 plus 1 upon 1 plus 1 and z is equal to 4 plus minus 2 upon 1 plus 1 and this is by section formula that is we have x is equal to now 2 plus 4 upon 1 plus 1 gives 3, y is equal to 3 plus 1 upon 1 plus 1 gives 2 and z is equal to 4 plus minus 2 upon 1 plus 1 gives 1. Therefore we have point R is 3 comma 2 comma 1 hence the position vector of R is given by 3 i cap plus 2 j cap plus k cap. So we have got our answer as 3 i cap plus 2 j cap plus k cap. Hope you have understood the solution. Bye and take care.