# Body Diagonals of a cube

1. Sep 1, 2006

### 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).

2. Sep 1, 2006

### 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

3. Jan 11, 2007

### overseastar

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

4. Jan 11, 2007

### 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.

5. Jan 11, 2007

### Gokul43201

Staff Emeritus
Last edited by a moderator: Apr 22, 2017
6. Jan 11, 2007

### overseastar

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

7. Jan 11, 2007

### overseastar

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

8. Jan 11, 2007

### overseastar

nvm, thx for your help~!

9. Jan 11, 2007

### Gokul43201

Staff Emeritus
Did you get the correct answer?

10. Jan 11, 2007

### 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.

11. Jan 12, 2007

### Gokul43201

Staff Emeritus
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.

12. Jan 12, 2007

### overseastar

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

13. Jan 12, 2009