A Point on Curve Where Tangent is Parallel How do I find a point on a curve, $r=\langle 2,3t,5t^3\rangle$ in which tangent line is parallel to some plane.
I thought to find the derivative first, but having trouble there as well. Anyway, this would provide the slope. However, I don't know what comes next.

A point on a curve $r(t)=\langle 1,t,t^2\rangle$ in which the tangent line is parallel to plane $x+2y+3z=0$ occurs where the derivative of $r(t)$ is orthogonal to the normal of the plane. That is, when $$r'(t)\cdot \hat{n}=0$$
$$\langle0,1,2t\rangle\cdot\langle1,2,3\rangle=0$$
