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 solve the problem of finding the position vector of point R that divides the line segment joining points P and Q in the ratio of 2:1, both internally and externally, we will follow these steps:

### Given:
- Position vector of point P, \( \vec{P} = \hat{i} + 2\hat{j} - \hat{k} \)
- Position vector of point Q, \( \vec{Q} = -\hat{i} + \hat{j} + \hat{k} \)

### (i) Finding R Internally

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