Struggling to begin answering the following question:
Let $L$ be the line given by $x = 3-t, y= 2+t, z = -4+2t$. $L$ intersects the plane $3x-2y+z=1$ at the point $P = (3,2,-4)$. Find parametric equations for the line through $P$ which lies on plane and is perpendicular to $L$.
So far, I know that I need to find some line represented by a vector $n$ which is orthogonal to $L$. So, with the vector of $L$ represented by $v$, I have:
$$n\cdot v = 0 \Rightarrow [a, b, c] \cdot [-1, 1, 2] = 0 \Rightarrow -a + b + 2c = 0$$
I am not sure how to proceed from here, or if I am even on the right track.