Here is the problem verbatim:(adsbygoogle = window.adsbygoogle || []).push({});

The polar and azimuthal angles of a vector are Θ_{1}and Φ_{1}. The polar and azimuthal angles of a second vector are Θ_{2}and Φ_{2}. Show that the angle ϒ between the two vectors satisfies the relation:

cos ϒ = cosΘ_{1}*cos Θ_{2}+sinΘ_{1}*sinΘ_{2}*cos(Φ_{1}-Φ_{2})

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= B_{x}x-hat+B_{y}y-hat+B_{z}z-hat using the x, y, and z spherical components. Someone please point me in the right direction.

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# I The angle between two vectors

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