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I The angle between two vectors

  1. Feb 7, 2016 #1
    Here is the problem verbatim:
    The polar and azimuthal angles of a vector are Θ1 and Φ1. The polar and azimuthal angles of a second vector are Θ2 and Φ2. Show that the angle ϒ between the two vectors satisfies the relation:

    cos ϒ = cosΘ1*cos Θ2+sinΘ1*sinΘ2*cos(Φ12)

    Hint: write out the Cartesian components of each vector in spherical coordinates and then evaluate the scalar product.

    Where I run in to trouble with this problem is when writing out the Cartesian components into Spherical components. I do know that x = ρ*sinΘ*cosΦ, y = ρ*sin Θ*sinΦ, and z=ρ cos Θ, but I'm not sure how to write a vector in the form of B= Bxx-hat+Byy-hat+Bzz-hat using the x, y, and z spherical components. Someone please point me in the right direction.
  2. jcsd
  3. Feb 7, 2016 #2
    I just realized I posted this in the wrong section of the forum. Sorry.
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