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 Solid Geometry - need help please

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T O P I C    R E V I E W
raghu Posted - 04/01/2008 : 13:14:29
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
4   L A T E S T    R E P L I E S    (Newest First)
Subhotosh Khan Posted - 04/01/2008 : 22:36:30
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.

raghu Posted - 04/01/2008 : 18:20:30
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.
raghu Posted - 04/01/2008 : 14:45:11
can you please expand on that.
Subhotosh Khan Posted - 04/01/2008 : 14:15:22
Express the diagonals as vectors - then use definition of vector product to find the angle.

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