If I have the parametric equation:
${x=t}$
${y=0}$
${z = 0 + -0.25x + 0.2x^2 + 0.1x^3}$
and I want to rotate it onto the plane:
$-{3x+y-2z = 0}$
how would I solve this problem? I know how to find the axis of rotation, but I can't seem to find a method to get the parametric equation on the new plane.
The axis of rotation would be normal to the normals of both planes. The original curve lies in the $x-z$ plane, which would have a normal of $[0, 1,0]$. The target plane has a normal of $[-3, 1, -2]$ so that means the axis of rotation would be $[0, 1, 0] \times [-3, 1, -2]$.