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I Unit vectors dot products

  1. Nov 6, 2016 #1
    Okay so I understand that in order to represent a vector which is in cartesian coordinates in spherical coordinates.. we use the transformation which is obtained by dotting the unit vectors.
    So my question goes like this:
    when we dot for example the unit vector ar^ with x^ we obtain sin(theta) * cos(phi), however can't the dot product be interpreted as the magnitudes multiplied by the cos of the angle between them.
    In this case the magnitudes are 1 cuz they are unit vectors but how can sin(theta) * cos(phi) equal cos(angle between ar^ and x^)
    I know my notation sucks plz pardon me it's my first time posting... I have no notation at all :(

    Thank you for the help
     
  2. jcsd
  3. Nov 6, 2016 #2

    Simon Bridge

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    If you identify the angle between ##\vec r = r\hat r## and ##\vec x = x\hat\imath## (you OK with i-j-k unit vectors?) for an arbitrary ##\vec r## as ##\alpha## to distinguish it from the ##\theta## and ##\phi## of the spherical polar coordinates... then ##\hat r\cdot \hat\imath = \cos\alpha## right?

    You can express ##\cos\alpha## in terms of ##\theta## and ##\phi##.
    Give it a go. ie. try first for ##\theta=\pi/2## and ##\phi >0##, then for ##\phi=0## and ##0<\theta<\pi/2## ... then combine the results.
     
  4. Nov 6, 2016 #3
    Awesome haha I actually got it :)
    thanks a million sir
     
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