Deck 13: Extension E: Vector Calculus

Question 1

Find (a)the divergence and (b)the curl of the vector field F.

Answer 1

(a).
(b).

Question 2

Let f be a scalar field.Determine whether the expression is meaningful.If so,state whether the expression represents a scalar field or a vector field.

Answer 2

The vector grad f is defined.It is the gradient (vector)field F of the scalar field f.So, ,which is not meaningful.

Question 3

Let f be a scalar field.Determine whether the expression is meaningful.If so,state whether the expression represents a scalar field or a vector field. curl f

Answer 3

The curl is a property of vector fields,not scalar fields.So,curl f is not meaningful.

Question 4

Let

Question 5

Find the curl of the vector field F.

A)
B)
C)
D)

Question 6

Let

A) 45
B) 9
C) 18
D) 27
E) None of these

Question 7

Find the divergence of the vector field.

Question 8

Find the curl of the vector field.

Question 9

Determine whether or not vector field is conservative.If it is conservative,find a function f such that

Question 10

Find the curl of the vector field.