Question

3: Express the vector "A" from point P (6, 0, -5) to Q (-1, 3, 7) in Spherical coordinate system and evaluate its curl.

Answer 1

Notice that in the second term the index originally on V has moved to the $ \Gamma$, and a new index is summed over. If this is the expression for the covariant derivative of a vector in terms of the partial derivative, we should be able to determine the transformation properties of $ \Gamma^{\nu}_{\mu\lambda}$ by demanding that the left hand side be a (1, 1) tensor. That is, we want the transformation law to be