- #1

raddian

- 66

- 0

## Homework Statement

Find the angle of the face diagonals of a (unit) cube.

I agree with this solution, but I have a problem with another face diagonal: the face diagonal from the angle (0,0,1),(0,0,0), and (1,1,1).

## Homework Equations

dot product

cos-1(a.b/ (|a||b|)

## The Attempt at a Solution

From the solution, we have an angle given from the points (1,0,1), (0,0,0), and (0,1,1).

Using the def. of dot product, if A is the vector (0,0,0) to (1,0,1) and B is the vector (0,0,0) to (0,1,1)

cos-1(A.B/(|A||B|)), where A.B = 1, |A| = |B| = sqrt(2).

Thus cos-1(1/ [ (sqrt(2)sqrt(2) ]) = 60 deg. Ok.

the face diagonal from the angle (0,0,1),(0,0,0), and (1,1,1):

A is the vector (0,0,0) to (0,0,1) and B is the vector (0,0,0) to (1,1,1)

cos-1(A.B/(|A||B|)), where A.B = 1, |A| = 1, |B| = sqrt(3).

thus cos-1(1/ [ sqrt(3) ]) != 60 deg.

Why is this happening?