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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[], 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.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf
    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!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf>
    https://brainmass.com/physics/mathematical-physics/finding-direction-cosines-16133

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