Finding points where a tangent line of a vector value function intersects a surface.

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I have no idea what to do with this problem, I can't find any advise online and my book is useless. The problem involves finding points where the tangent line of a vector value function intersects with a surface. The vector valued function is $r(t)=\langle 2+t^3, 2t-2, t^2\rangle$ and the surface is $z=x^2-y.$ Any help is appreciated, have a nice day.