Show that the lines

$L_1$:$($:$x,y,z$:$)=($:$6,-7,2$:$)t($:$3,6,-3$:$)$

$L_2$:$($:$x,y,z$:$)=($:$2,1,-6$:$)t($:$-5,-10,5$:$)$

are different and parallel and find an equation of the plane they determine.