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# Finding the Direction Cosines

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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[&#61537;], cos[&#61538;] and cos [&#61543;], where &#61537; is the angle between A and x , where &#61538; is the angle between A and y, and &#61543; is the angle of A and z.

b) Show that the direction cosines obey the relationship (cos[&#61537;])2+(cos[&#61538;])2+(cos [&#61543;])2.

https://brainmass.com/physics/mathematical-physics/finding-direction-cosines-16133

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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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!