Finding Intersection and Tangent Lines of Parametric Curves | Step-by-Step Guide

[autre]

I need to find the point of intersection of the curves x^2 + y^2 =1, z= 0 and x=cost, y=sint, z=t. I plugged in the latter equation into the former and got (1,0,0) as an answer but I'm not exactly sure why that works, I can't visualize how plugging in the parts of a parametric equation will yield the point of intersection.

I also need to find the tangent lines to the curves at that point, and I'm not sure where to start.

 

[hunt_mat]

The two curves you have in the circle in the plane and a helix. You would expect that there is only one intersection point, and that will be at t=0.

 

[autre]

Makes sense. How do I find the tangent line to a parametric curve in R3, though?

 

[hunt_mat]

Differentiate with respect to t!