A line passes through the points with position vectors are $\hat i+\hat j-2\hat k$ and $\hat i-3\hat j+\hat k$. The position vector of a point on the line which is at a unit distance from the first point is ?

Question

$\begin{array}{1 1} (a)\:\frac{1}{5}(6\hat i+\hat j-7\hat k)\:\qquad\:(b)\:\frac{1}{5}(4\hat i+9\hat j-13\hat k)\:\qquad\:(c)\:\frac{1}{5}(\hat i-4\hat j+3\hat k)\:\qquad\:(d)\:None\:of\:these. \end{array} $