Its been a little while since I've done these ones and I'm having a little trouble wrapping my head around this one.
Find the equation of the plane perpendicular to the line tangent to r(t)=(3sint)i - (2cost)j + (t)k at t=pi/2.
Would the normal vector to the plane simply be the above vector? But then would I use (0,0,0) as a point in the plane?
First find the unit tangent vector to the curve.
Then find the unit normal using,
The vector equation of the plane perpendicular to the tangent line would then be,
where represent the position vector of any point in the plane.
Hope this helps you to solve the problem.