Find the position vector of the mid-point of the vector joining the points and

The position vectors of two points A and B are and respectively. Find the position vector of a point C which divides AB externally in the ratio 1 : 2. Also, show that A is the mid-point of the line segment CB.

Find the position vector of a point R which divides the line joining A(-2, 1, 3) and B(3, 5, -2) in the ratio 2 : 1 (i) internally (ii) externally.

If and A(1, 2, -1) is the given point, find the coordinates of B.

Write a unit vector in the direction of where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.