A and B are two points with position vectors 2→a + 3→b and 6→b - →a respectively. Write the position vector of a point P which divides the line segment AB internally in the ratio 1:2.

Given:
−−→OA = 2→a + 3→b
−−→OB = 6→b - →a
Since P divides AB in 1:2 internally, so,
−−→OP = (1.−−→OB + 2.−−→OA) / (1+2)
= (1 (6→b - →a) + 2 (2→a + 3→b)) / 3
= (6→b - →a + 4→a + 6→b) / 3
= (3→a + 12→b) / 3
Therefore,
−−→OP = →a + 4→b