This is a problem that I am having trouble figuring out in my Differential Geometry course. Here it is below:

Demonstrate that the curve

r(t) = <a(sint)^2, asin(t)cos(t), acos(t)>

lies on a sphere and that all normal planes pass through the origin.

I think r(t) is a vector, but my teach really didn't give too much information on it and I am curious. Could someone help me with this problem? Try to show it and detail so that I can understand it, since this is a relatively new topic for me. Thanks.