Consider two points P and Q with position vectors ` -> O P=3 -> a-2 -> b`and ` -> O Q= -> a+ -> b`Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.

Explanation

To find the position vector of point R that divides the line joining points P and Q in the ratio 2:1, we will solve the problem in two parts: (i) for internal division and (ii) for external division.

### Given:
- Position vector of point P: \( \vec{OP} = 3\vec{a} - 2\vec{b} \)
- Position vector of point Q: \( \vec{OQ} = \vec{a} + \vec{b} \)

### (i) Internal Division

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