Question

Does the line [x,y,z]=[5,-9,3]+k[1,-12,2] intersect the plane [x,y,z]=[4,-15,8]+s[1,-3,1]+t[2,3,1]? If so, how many solutions are there?

( I tried finding the normal vector, there after finding the "d" value to write in scalar equation, and once it is in scalar equation i wrote the line in parametric form and substituted it in the scalar equation, but I don't seem to get the answer, is that the correct method?)