P and Q are two points with position vectors 3→a + 2→b and →a + →b respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

Position vector of P = 3→a + 2→b
Position vector of Q = →a + →b
Point R divides segment PQ in ratio 2:1 externally.
Position vector of R = (Position of P)1 - (Position of Q)2 / 1 - 2
Position vector of R = (3→a + 2→b)1 - (→a + →b)2 / 1 - 2
= 3→a + 2→b - 2→a - 2→b / -1
= →a / -1
= -→a
Therefore, position vector of R = -→a