Finding the Direction Cosines
Okay I have been racking my brain with this one for over a week and still have no clue how to do this.I need to study this for a test I am having and can't seem to figure this out
Consider an arbitrary 3D vector: A=Axx+Ayy+Azz
a) Determine the direction cosines for this vector. These are cos[], cos[] and cos [], where  is the angle between A and x , where  is the angle between A and y, and  is the angle of A and z.
b) Show that the direction cosines obey the relationship (cos[])2+(cos[])2+(cos [])2.
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Please see the attached document..
Consider an arbitrary 3D vector: A=Axx+Ayy+Azz
a) Determine the direction cosines for this vector. These are cos[], cos[] and cos [], where is the angle between A and x , where is the angle between A and y, and is the angle of A and z.
The components are, Ax Ay and Az
Direction cosines are
cos[] = Ax/|A|
cos[] = Ay/|A|
cos [] = Az/|A|
Where |A| = [Ax2 +Ay2+Az2]1/2
(I have included an example also at the end)
b) Show that the direction cosines obey the relationship (cos[])2+(cos[])2+(cos [])2 = 1
(cos[])2+(cos[])2+(cos [])2 = [Ax/|A|]2 + [Ay/|A|]2 + [Az/|A|]2
= [Ax2 +Ay2+Az2]/|A|2
= [Ax2 +Ay2+Az2]/ [Ax2 +Ay2+Az2]
= 1 result
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