Formula of angle between longest diagonal and any edge of a cube Let $a<b$ be real numbers. Define a cube $Q$ in $R^n$ to be the $n$-fold Cartesian product of $[a,b]$ with itself. Find a formula of the angle between the longest diagonal of $Q$ and any of its edges. 
I am not sure where to start. Any help would be appreciated.

To get the length of the diagonal, the Pythagorean theorem works in any dimension.  See the section "Euclidean distance in various coordinate systems".  Add up the squares of the length in each dimension, take the square root of the sum, and you are there.  Then, as Trevor says, take the dot product of a side with the diagonal to find the angle.
To be more explicit, imagine the cube with one corner at the origin and sides going out along the positive directions.  The angle will be the same for all cubes.  The length of the diagonal is $\sqrt{n}$.  The dot product of the diagonal with a side is 1.  So $\theta=\arccos \left (\frac{1}{\sqrt{n}}\right)$
