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Topic: Help on tetrahedrons
Replies: 1   Last Post: Jun 16, 1996 6:03 PM

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Posts: 14
Registered: 12/12/04
Re: Help on tetrahedrons
Posted: Jun 16, 1996 6:03 PM
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In article <4poknv$>, (Hauke Reddmann) writes:
> Maciej Kosinski ( wrote:
> : How to prove that the angule of the regular tetrahedron is 109
> : degrees (or was it 109,5 degrees) in NH3 molecule?
> Old trick: Use CH4 instead. All coordinates must sum to zero
> by symmetry, so if one H is at (1,0,0), the rest is at (-1/3,?,??).
> You make take ? as 0. Apply vector cosinus. cos(angle)=-1/3.Done.

A better idea is to note that the points with co-ords
(1,1,1) (1,-1,-1) (-1,1,-1) (-1,-1,1)
are the vertices of a tetrahedron centered at the origin.

Use the dot product to obtain cos(t) = -1/3

Ian H

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