Consider the vector field: F = (ex, In(xy), e xyz) (i) Find div(F) (ii) Find curl(F) (iii) Find div(curl(F))

Consider the vector field v(x) j+6k. a) Calculate fv• dr, where I is the straight line from (4,0,4) to (0,4,8). b) Calculate fu• dr where C'is the curve from (4,0,4) to (0,4, 8) in the first quadrant given by x? + 4y? = 22 ,x + z = 8.

Show that Green's Theorem holds for the vector fieldF(x, y)=(x +y, 3x) at a square of side 2.

Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical variables.