Q) A particle's position at time t is determined by the equation of the helix

r(t) = < cost, sint, t>

Let P be a point with a coordinates (0,1,pie/2).

1. Find the curvature k(t) at any time t.

2. Find the center of the osculating circle at P.

3. Write down teh equation of teh osculating plane and the sphere whose intersection with that plane is the osculating circle.

4. Find a parametric equation of the osculating circle at P.

5. Find the acceleration normal vector and tangential acceleration tension vector components of the acceleration vector at P.

If any of you can do these problems, I would appreciate your help. I started finding curvature but i didn't know how to find the curvature with just the vector equation. I thought i needed y = f(x) equation to find curvature. Can anybody answer this by doing number 1 and so on?

Thank you so much in advance!