Space geometry

1003233605

Level: 
C
We are given skew lines p and q. p:x=1−t,q:x=1−2s,y=1+t,y=s,z=3+2t; t∈R,z=3+3s; s∈R. Find parametric equations of a straight line r, that is intersecting both lines p and q and lying in the plane x+2y−z+2=0.
r:x=−1+2m,y=3−3m,z=7−4m; m∈R
r:x=−1+m,y=3+3m,z=7−m; m∈R
r:x=−1+3m,y=3+2m,z=7+5m; m∈R
r:x=−1+m,y=3−m,z=7+m; m∈R

1003233607

Level: 
C
Determine the relative position of three planes: α: 2x+y+9z−18=0,β: x+3y+2z+16=0,γ: x+2y+3z+6=0.
Planes α, β and γ intersect in a straight line.
Each of the two planes are intersecting and the lines of intersection are three different lines parallel to each other.
All three planes intersect at just one point.