Radius of A Circle inside a Sphere

  • Thread starter PAR
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  • #1
PAR
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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 [Broken]

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!
 
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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi PAR! :wink:

Yes, rcosθ. :smile:
 

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