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 Solid Geometry - need help please
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raghu
Senior Member

USA
37 Posts

Posted - 04/01/2008 :  13:14:29  Show Profile  Reply with Quote
there is a cube. Two diagonals from the same vertex are drawn, one as face diagonal and the other as space diagonal. Find the measure of angle between the two diagonals.
This is how I started .
I assumed a 1X1x1 cube. face diagonal came out as sqrt(2) and Space Diagonal came out as sqrt(3). I tried to apply sine rule. There are too many unknowns and hit a brick wall.
Appreciate any help
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 04/01/2008 :  14:15:22  Show Profile  Reply with Quote
Express the diagonals as vectors - then use definition of vector product to find the angle.
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raghu
Senior Member

USA
37 Posts

Posted - 04/01/2008 :  14:45:11  Show Profile  Reply with Quote
can you please expand on that.
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raghu
Senior Member

USA
37 Posts

Posted - 04/01/2008 :  18:20:30  Show Profile  Reply with Quote
Here is how I solved the problem. Face diagonal will be of size sqrt(2) and space diagonal will be sqrt(3).
The angle between the two diagonals will be sine inverse of (1/sqrt3). So the angle is 60 degrees.
Mr. Khan,
thanks for the response.
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 04/01/2008 :  22:36:30  Show Profile  Reply with Quote
quote:
Originally posted by raghu

Here is how I solved the problem. Face diagonal will be of size sqrt(2) and space diagonal will be sqrt(3).
The angle between the two diagonals will be sine inverse of (1/sqrt3)

correct

. So the angle is 60 degrees.incorrect

sin-1(1/3) = 35.26438968

Mr. Khan,
thanks for the response.

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