Question

r=<3,3,0>+t<3,-3,1> r=<6,0,1>+s<-3,3,0>
find a point at which the given lines intersect

Answer 1

Try translating the two equations into their component forms, like this:
\[<3,3,0>+t<3,-3,1> becomes x _{1}=3+3t, y _{1}=3-3t... etc.\]
do that to both equations and then equate (that is set equal) the x, y, and z terms from each r equation. That may give you a start.

Answer 2

Sorry about the equation cut-off, my first few posts here... so not used to it yet. Anyways that process will give you 3 equations in 2 unknowns to solve.