Vector operations

So, for example, to take the dot product of two vectors in spherical coordinates, we would do the following (warning: remember that these are in {ρ,φ,θ} form):

DotProduct[{1, π/2, π/6}, {2, π/2, (2π)/3}, Spherical]

0

If we use Cartesian coordinates, we get:

DotProduct[{1, π/2, π/6}, {2, π/2, (2π)/3}, Cartesian]

2 + (13 π^2)/36

CrossProduct[{1, π/2, π/6}, {2, π/2, (2π)/3}, Spherical]

{2, 0, 0}

CrossProduct[{1, π/2, π/6}, {2, 0, (2π)/3}, Spherical]

{2, π/2, -π/3}

Problem

Created by Mathematica  (October 18, 2004)