the vector fields F with the plots labeled I-IV, Then give a one sentence description of the vector field would look like if you plotted it. F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin
I: F(x, y) = (y, x) - This vector field corresponds with plot I, as it forms a series of counter-clockwise circular paths.
II: F(x, y) = (1, sin y) - This vector field corresponds with plot II, as it forms a series of parallel lines.
III: F(x, y) = (x - 2, x + 1) - This vector field corresponds with plot III, as it forms a series of diagonal lines that move outward from the origin.
IV: F(x, y) = (y, 1/x) - This vector field corresponds with plot IV, as it forms a series of concentric circles with the origin as their center.
F(x, y) = (x, y): rot(F) = 0; The vector field would look like a grid of straight lines.
F(x, y) = y i = x j: rot(F) = 1; The vector field would look like a series of counter-clockwise circular paths.
F(x, y) = (y, -x): rot(F) = -1; The vector field would look like a series of clockwise circular paths.
F(x, y) = (1 + xy)i + x^2 sin y j: rot(F) = x^2; The vector field would look like a series of curves that rotate counter-clockwise around the origin.
F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin
Learn more about vector field here
brainly.com/question/14122594
#SPJ4
