Direction Angles: Example - Sum of Squares of Cosines

   Example   The cosines of the direction angles of  (–1,1,1)  in    are

To see this, we need  x , together with the formula

cos (1/|x|) · (e x).

Alternatively, we can inspect the diagram below

and conclude that, up to a sign, all direction angles are equal:

cos cos cos;    so  |cos| 1/.

Inspection of the diagram determines the sign of  cos.

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