Angle between diagonals of a cube

[BoundByAxioms]

Homework Statement

Find the acute angle between two diagonals of a cube.

Homework Equations

N/A

The Attempt at a Solution

I know that the length of a diagonal of a cube whose side lengths are each one is sqrt(3), so I think it has something to do with that. Other than that, I'm drawing a blank. I could use the unit vectors <1,0,0> and <0,1,0> and find the angle between them, but that's not giving me the right answer.

 

[Defennder]

Here's something you can try. Locate the cube on a coordinate axis, and determine the coordinates of is corners. Then find the vectors corresponding to the cube diagonals and make use of the definition of the dot product.

 

[benorin]

Draw a cube and sketch in a face diagonal and a space diagonal.
Then draw two triangles and smile.