3. Determine if the vector field F(x, y, z) = e" sin yzi + ze² cos yzj + ye² cos yzk is conservative or not. If it is, find the potential function f such that F = Vf.

Find the work So F. dr done by the force field F = (y, x, z) on a particle that moves along C the line segment from (1, -3, 2) to (4, 6,-5).

Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0 ={8/ B(r) = where r = √x² + y2 is the distance to the z-axis and B is a constant that depends on the current strength I and the spacing of the turns of wire. The vector potential for B is -{} J A(r) = if r> R Bk if r R r< R S

Consider the vector field F(x, y, z) = y cos (xy)i+(x cos(ry) – sin ye*)j+sin ye k (4) Find a function f such that F = Vf.