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raghu
Senior Member

USA
37 Posts

 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

Subhotosh Khan
Advanced Member

USA
9117 Posts

 Posted - 04/01/2008 :  14:15:22 Express the diagonals as vectors - then use definition of vector product to find the angle.

raghu
Senior Member

USA
37 Posts

 Posted - 04/01/2008 :  14:45:11 can you please expand on that.

raghu
Senior Member

USA
37 Posts

 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.

Subhotosh Khan
Advanced Member

USA
9117 Posts

 Posted - 04/01/2008 :  22:36:30 quote:Originally posted by raghuHere 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.incorrectsin-1(1/3) = 35.26438968Mr. Khan,thanks for the response.
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