Understanding Body Diagonals of a Cube

[Disar]

Can anyone out there tell me what the body diagonals of a cube are.
I am asked to find the angle between the body diagonals of a cube. Seeing as how it is just the application of the dot product it does not seem difficult other than I do not know what body diagonals are (I have an idea but would like to know from someone for sure).

 

[Disar]

Found it! The body diagonals of a cube are the from one point on a cube to the next and the angle between them is 90 degrees (they bisect one another)
Should of looked first

 

[overseastar]

I have the same problem, yet, I still can't picture it.

 

[tim_lou]

slice the cube through the intersecting diagonal... the shape that is left is like an "incline plane". or imagine a table with square top, and square sides and square base with the legs intersecting.

 

[Gokul43201]

I have the same problem, yet, I still can't picture it.

It's the thing in these pictures:

http://library.thinkquest.org/22494/images/cubi.jpg

http://www.mathaware.org/mam/00/master/essays/B3D/2/JPG/figure16.jpg

In the second picture, it's the "longer diagonal".

 

[overseastar]

I seem to be getting an answer of 45 degrees which isn't right...

 

[overseastar]

When drawing the vectors in the case within the cube, do they have to be from the same origin?

 

[overseastar]

nvm, thanks for your help~!

 

[Gokul43201]

Did you get the correct answer?

 

[overseastar]

i used a unit cube.
with one diagonal at (0 0 1) (1 1 0)
the other diagonal at (0 0 0) (1 1 1)
but it doesn't work, hmmm...for a sec i thought i did get it.

 

[Gokul43201]

i used a unit cube.
with one diagonal at (0 0 1) (1 1 0)
the other diagonal at (0 0 0) (1 1 1)

Good, now find the vectors describing the diagonals using the vectors given above, representing their end-points.

but it doesn't work, hmmm...for a sec i thought i did get it.

What do you mean by "it doesn't work"? What doesn't work?

The answer written by Disar is incorrect.

 

[overseastar]

oh, if that's the case, I think I got it LOL Thanks a bunch!

 

[Cosmo Cookie]

I went to my professor about this problem and he told me to use A=x+y+z and B= -x+y+z, naming one of the body diagonals A, and the other body diagonal B. I'm a bit confused how to take the 4 points above to make them fit the A and B my prof gave me. Can anyone help me with this please?? Thanks

 

[striker089]

Good, now find the vectors describing the diagonals using the vectors given above, representing their end-points.

What do you mean by "it doesn't work"? What doesn't work?

The answer written by Disar is incorrect.

Can you help me? I still don't get it, thanks