11. Let fbe a scalar function ofx, y, and z, 1.e.. f=f(x, y, z), and let F be a
ID: 1770152 • Letter: 1
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11. Let fbe a scalar function ofx, y, and z, 1.e.. f=f(x, y, z), and let F be a vector (vector field), ie. F = Fil + Fyj + Fek . For each of the following operations, indicate if the result is (i) a scalar/scalar function, or (ii) a vector/vector field, or (iii) some mathematical entity, other than a scalar/scalar function or a vector/vector field (e.g., an integral, delta function, time-evolution or time-reversal operator, a quantized string), or (iv) a meaningless expression (not defined) For example, ·c is a scalar. but x c is a vector Check only one box in each row below. Justifications are not required. Scalar or scalar function Vector or vector field Some other mathematical entit Meaningless expression cur div f gradf curl F divF grad F div(gradf) curl(div f) Fx curl FExplanation / Answer
curl f : meaningless expression
divf f : meaningless expression
grad f: vector field
curl F : vector field
div F : scalar field
grad F : Some other mathematical entity/ tensor
div(grad f) : scalar field
curl ( div f) : meaningless, divergence of a scalar field cannot be taken
| F x curl F | : Some other mathematical entity, magnitude of the resultant vector will just be a number
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