Which of the following expressions are meaningful, and which are nonsense? For t

Question

Which of the following expressions are meaningful, and which are nonsense? For those which are meaningful, decide whether the expression defines scalar function or a vector field. State the reason why if it is nonsense. a. curl(grad f) b. grad(curl f) c. div(grad f) d. grad(div f) e. curl(div f) f. div(curl f)

Explanation / Answer

for f being a scalar a) meaningful vector grad f = vector -> curl of vector = vector b) nonsense can't take curl of scalar c) meaningful scalar grad f = vector -> div of vector = scalar d) nonsense can't take div of scalar e) nonsense can't take div of scalar f) nonsense can't take curl of scalar

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