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Angle between diagonals of a cube

  • #1

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.
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
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.
 
  • #3
benorin
Homework Helper
Insights Author
Gold Member
1,234
61
Draw a cube and sketch in a face diagonal and a space diagonal.
Then draw two triangles and smile.
 

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