Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ` hat i+2 hat j- hat k`and `- hat i+ hat j+ hat k`respectively, in the ratio 2 : 1(i) internally (ii) externally

Explanation

To find the position vector of point R that divides the line joining points P and Q in the given ratios, we will follow the steps for both internal and external division.

### Given:
- Position vector of P, **OP** = \( \hat{i} + 2\hat{j} - \hat{k} \)
- Position vector of Q, **OQ** = \( -\hat{i} + \hat{j} + \hat{k} \)
- Ratio = 2:1

### (i) Internal Division
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