How to plot a given vector field A(x y,z)=(-y)x hat + ( x) y hat + (0) z hat in x y plane .I tried this code but getting an error

Question

OMEIR HUSSAIN 2024-1-28

回答： VBBV 2024-1-28

 % Define the vector field A(x, y, z) = (-y)x_hat + (x)y_hat + (0)z_hat
syms x y z
A = [-y*x, x*y, 0];

% Define the x and y coordinates for the plot x = linspace(-2, 2, 20); y = linspace(-2, 2, 20); [X, Y] = meshgrid(x, y);

% Evaluate the vector field at each point on the grid U = subs(A(1), {x, y}, {X, Y}); V = subs(A(2), {x, y}, {X, Y});

% Plot the vector field quiver(X, Y, U, V); xlabel('x'); ylabel('y'); title('Vector Field Plot in the x-y Plane');

Answer 1

VBBV 2024-1-28

% Define the vector field A(x, y, z) = (-y)x_hat + (x)y_hat + (0)z_hat

syms x y z

A = [-y*x, x*y, 0];

xx = linspace(-2, 2, 20);

yy = linspace(-2, 2, 20);

[X, Y] = meshgrid(xx, yy);

U = subs(A(1), {x, y}, {X, Y});

V = subs(A(2), {x, y}, {X, Y});

quiver(X, Y, U, V); xlabel('x'); ylabel('y');

title('Vector Field Plot in the x-y Plane');