Please check my work for the following problem:
Find the point(s) where the curve r = <t,t2,-3t> intersects the plane 2x-y+z=-2.
2. The attempt at a solution
t + t2 -3t = -2
(t-2)(t+0) = -2
t=0 and t=-2
plugging those values in yields: r(0) = <0,0,0>
r(-2) = <-2,4,6>
Is that what the problem is asking for?