# 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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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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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