Deck 13: Extension A: Vector Calculus

Question 1

Which plot illustrates the vector field

A)
B)
C)
D)

Answer 1

Question 2

Find the gradient vector field of

Answer 2

Question 3

The flow lines (or streamlines)of a vector field are the paths followed by a particle whose velocity field is the given vector field.Thus,the vectors in a vector field are tangent to the flow lines.The flow lines of the vector field satisfy the differential equations and Solve these differential equations to find the equations of the family of flow lines.

Answer 3

Question 4

A particle is moving in a velocity field At time t = 1 the particle is located at the point (1,5,5).
a).What is the velocity of the particle at t = 1?
b).What is the approximate location of the particle at t = 1.01?

Question 5

Find the gradient vector field of f.

A)
B)
C)
D)
E) None of these