Discussion
Match the operator with what it takes and returns.
1. Gradient 2. Divergence 3. Curl
P. Vector to scalar Q. Vector to vector R. Scalar to vector
Answer: D
Keeping these three straight prevents most of the errors in field theory: a divergence can never have a direction and a gradient can never be applied to a vector. It also explains at once why the Laplacian of a scalar is a scalar.
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