Question

Looking for different ways to find the diagonal between the two furthest corners on a cube just for fun. :D

Answer 1

The weirder the better.

Answer 2

vector sum, I think

Answer 3

@Astrophysics help!

Answer 4

here is another formula, which uses the vector product and scalar product, between the sides of the cube treated as vectors:
\[\Large D = \sqrt {3{l^2}} = \sqrt {3{V^{2/3}}} = \sqrt {3\left\{ {\left( {{\mathbf{l}} \times {\mathbf{l}}} \right) \cdot {\mathbf{l}}} \right\}} \]
where \(V\) is the volume, and \(D\) is the diagonal, furthermore \(l\) is the side of the cube or the magnitude of the vector \(\mathbf{l}\)

Answer 5

oops.. I have made a typo:
\[\Large D = \sqrt {3{l^2}} = \sqrt {3{V^{2/3}}} = \sqrt {3{{\left\{ {\left( {{\mathbf{l}} \times {\mathbf{l}}} \right) \cdot {\mathbf{l}}} \right\}}^{2/3}}} \]