1. The problem statement, all variables and given/known data 1. Suppose r(t)= (e^t * cost) i + (e^t * sint) j. Show that the angle between r and a never change. What is the angle. 2. Find the equations for the osculating, normal, and rectifying planes of the curve r(t)=t i + t^2 j + t^3 k. 3. Express the curvature of a twice differentiable curve r= f(theta) in the polar terms of r and its derivatives 2. Relevant equations Kappa, Torsion, cross product, dot product,... 3. The attempt at a solution 1. So a is the acceleration. Thus, it is the 2nd derivative. So do I find the normal vector of r and a and then take their cross product to find the angle ? What will be the normal vector to r ?? 2. So is the osculating plane pretty much the curvature circle ? What is the rectifying plane ? 3. I am kinda lost in the problem. How should I attack this ?