Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `2( veca+ vec b)`and `( vec a-3 vec b)`externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

Explanation

To find the position vector of point R that divides the line joining points P and Q externally in the ratio 1:2, we can follow these steps:

### Step 1: Identify the position vectors of points P and Q
Given:
- Position vector of point P, \( \vec{P} = 2\vec{a} + \vec{b} \)
- Position vector of point Q, \( \vec{Q} = \vec{a} - 3\vec{b} \)

### Step 2: Use the formula for external division
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