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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I can understand it intuitively, but can't prove mathematically...Can you help me??

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- Thread starter Flotensia
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- #1

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I can understand it intuitively, but can't prove mathematically...Can you help me??

- #2

Ray Vickson

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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I can understand it intuitively, but can't prove mathematically...Can you help me??

PF rules forbid us from offering help until you have demonstrated an effort and shown your work.

- #3

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- #4

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If you use 3 parameters to parametrize a region of space in ℝ

However, if you only use 2 parameters to parametrize a region of space in ℝ

- #5

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Ahh, I got what 2 parameters mean. Thanks. then could you help me more to solve that problem??

- #6

Dick

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Ahh, I got what 2 parameters mean. Thanks. then could you help me more to solve that problem??

You know that the partial derivatives are tangent vectors, right? And you know that the cross product is orthogonal to the two vectors, I hope. And dot products are related to cosines of the included angle and cross products are related to sine? Put all of those ingredients together.

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- #8

Dick

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Look at the denominator in terms of the included angle ##\theta##. Use ##1-\cos^2(\theta)=\sin^2(\theta)##. Now does that help?

- #9

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I was so silly. It helps me a lot. Thanks for your help!!

- #10

Dick

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I was so silly. It helps me a lot. Thanks for your help!!

A nudge is a good as a wink. And you are welcome!

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