Question

One common parameterization of the sphere of radius 1 centered at the origin is r ⃗(u+v)=sin⁡u cos⁡v i ⃗+sin⁡u sin⁡v j ⃗+cos⁡u k ⃗ Find formulas for the two unit normal to the sphere at parameter values (u,v). The algebra will look a little bit intimidating, but things actually simplify nicely, particularly if sin(u) is factored from each component of the normal vectors, and the remaining vector portion is compared to the original r ⃗(u,v).

Answer 1

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