Find the equation of the line in vector and in cartesian form that passes through the point with position vector $2\hat{ i}- \hat{j} + 4\hat{k}$ and is in the direction$\hat{i} + 2\hat{j} - \hat{k}$.

Question

$\begin{array}{1 1}(2 \hat i-\hat j+4 \hat k)+t(\hat i+2 \hat j -\hat k) \\ (2 \hat i-\hat j+4 \hat k)-t(\hat i+2 \hat j -\hat k) \\ (4 \hat i-\hat j+4 \hat k)+t(\hat i+2 \hat j -\hat k) \\ (2 \hat i-\hat j+4 \hat k)+t(\hat i+5 \hat j -6\hat k) \end{array}$