A plane is determined by $(x,y,z) = (1,-1,0) + t(1,-1,2)$ and point $p(1,2,3)$. find point of intersection of $(1,4,-1)+s(-6,2,-4)$ with this plane.
I tried this: given the data plane equation is:$$ (x,y,z) = (1-,1,0) + t(1,-1,2)+w(1-1,2+1,3-0)= (1-,1,0) + t(1,-1,2)+w(0,3,3)$$ In Cartesian representation this is:$$ 3x+y-z=2 $$ general point of the line is: $(1-6s,4+2s,-1-4s)$. we'll substitute that into $3x+y-z=2$, yielding $s=2$, hence point of intersection is $(-7,8,-9)$. this doesn't match the answers though..