Let P and Q be two points with position vectors 3a − 2b and a + b respectively. The position vector of a point R which divides the line joining P and Q in the ratio 2:1 internally is:

Let P and Q be two points with position vectors 3a − 2b and a + b respectively. The position vector of a point R which divides the line joining P and Q in the ratio 2:1 internally is:

• A. (5a)/3
• B. (5a + b)/3
• C. (a + 4b)/3
• D. 2a

Answer: A) (5a)/3

Explanation: By section formula: r = (2(a + b) + 1(3a − 2b)) / (2 + 1) = (2a + 2b + 3a − 2b) / 3 = 5a / 3.