Exam 13: Extension A: Vector Calculus

Which plot illustrates the vector field

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.

Find the gradient vector field of

Find the gradient vector field of f.

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?