Answer:
AB = b - a
Explanation:
AB = -OA + OB
AB = -a + b we usually write the positive vector first
AB = b - a
We know that P divides AB in the ratio 3:1 so PB = 1/4 AB
AB is negative as we are going in the opposite direction
OP = OB - 1/4 AB
OP = b - 1/4 (b - a)
multiplying inside the brackets:
OP = b - 1/4b + 1/4a
OP = 3/4b + 1/4a