The position vectors of two points A and B are \(\hat{i}+\hat{j}\) and \(\hat{j}+\hat{k}\) respectively. If point C divides the line section AB in the ratio 2 ∶ 1, then the position vector of C is

Concept:

Let \(\vec a, \vec b\) be the position vector of A, B respectively. Then the position vector of P which divides AB in the ratio m:n is \(m\vec b+n\vec a\over m+n\)

Explanation:

Position vector of A is \(\hat{i}+\hat{j}\) and B is \(\hat{j}+\hat{k}\)

C divides AB in the ratio 2:1

Hence position vector of C is \(2(\hat j+\hat k)+1(\hat i+\hat j)\over 2+1\) = \(\hat i+3\hat j+2\hat k\over 3\) 

(3) is correct