1. You've 3 lines:

x,y,z)=s \cdot (1,2,1)" alt="l_1x,y,z)=s \cdot (1,2,1)" />

x,y,z)=(9,6,0) + t \cdot (0,1,-1)" alt="l_2x,y,z)=(9,6,0) + t \cdot (0,1,-1)" />

and a line which passes through a point of in the direction of (-3, 1, 1).

x,y,z)= s \cdot (1,2,1) + r \cdot (-3,1,1)" alt="l_3x,y,z)= s \cdot (1,2,1) + r \cdot (-3,1,1)" />

2. Line passes through a point of :

Solve for (r, s, t).

3. For confirmation only: I've got