Question

Find intersection of the lines
l1: r=(2,1,0) + t(1,-1,1)
l2: r=(3,0,1) + s(2,3,-1)

Answer 1

Please try to re-write your lines with cartesian equations

Answer 2

Set the vectors equal to each other:\[\begin{align*}\langle2,1,0\rangle+t\langle1,-1,1\rangle&=\langle3,0,1\rangle+s\langle2,3,-1\rangle\\
\langle2+t,1-t,t\rangle&=\langle3+2s,3s,1-s\rangle
\end{align*}\]
This gives the following system\[\begin{cases}2s-t=-1\\
3s+t=1\\
s+t=1\end{cases}\]