The parametric line equations are:
\(\displaystyle L_{1}: \;\ x=3+t, \;\ y=1-t, \;\ z=3t\)
\(\displaystyle L_{2}: \;\ x=2t, \;\ y=-2+2t, \;\ z=5-t\)
\(\displaystyle v_{1}=(1,-1,3), \;\ v_{2}=(2,2,-1)\) are parallel to the lines.
Start by finding the cross product of v1 and v2:
L1 contains the point (3,1,0) and is parallel to the vector (1,-1,3)
The cross product is \(\displaystyle n=\begin{vmatrix}i&j&k\\1&-1&3\\2&1&-1\end{vmatrix}=-2i+7j+3k\)
Now, use either point, along with n, to set up the plane equation
