Author 
Topic 

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 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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