Find the equation of a line (in vector and cartesian form) that passes through the point of intersection of lines \( \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = z \) and is parallel to the vector \( 3\hat{i} + 2\hat{j} - 8\hat{k} \).