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 externally is :

$3\hat i+3\hat j-3\hat k$

The correct answer is option (2) → $3\hat i+3\hat j-3\hat k$

dividing into 2 : 1 externally is equivalent to dividing in 2 : -1

so $\frac{2(\hat{i} + 2\hat{j} - \hat{k})-1(-\hat{i} + \hat{j} + \hat{k})}{2-1}$

$=\frac{3\hat i+3\hat j-3\hat k}{1}$

$=3\hat i+3\hat j-3\hat k$