Radius of A Circle inside a Sphere

[PAR]

Homework Statement

Say you have a sphere of radius r centered at the origin, and a vector v <r,0,0>.

Let v' be the vector v rotated about the y-axis by angle theta.

What is the shortest distance between the end of the vector and the z-axis?

Homework Equations

The Attempt at a Solution

I drew a picture:

[PLAIN]http://img253.imageshack.us/img253/9459/circleinsphere.png

Obviously the shortest distance would be the line normal to the z-axis that would complete a right triangle with the y-axis and the vector v'. The distance is also equal to the radius of a circle, which I drew on the picture.

Because of this, I believe the answer is r*cos(theta), however I am not sure, and I need to know this for a programming assignment. Thank You!

 

[tiny-tim]

Hi PAR!

Yes, rcosθ.