Inconsistency between sizes of second and third arguments

Hi, I am getting an error while calculating work done with a given vector and parameter. How to rectify that?

F=subs(f,{x,y},r);        % Inconsistency between sizes of second and third arguments
Fdr=sum(F.*dr);           % [X2,Y2,symX,symY] = normalize(X,Y);


% My code is below:

clc
clear all
syms x y t
f=input('Enter the components of 2D vector function [u,v] ');
r=input('Enter x,y in parametric form');
I=input('Enter the limits of integration for t in the form [a,b]');
a=I(1);b=I(2);
dr=diff(r,t);
F=subs(f,{x,y},r);
Fdr=sum(F.*dr);
I=int(Fdr,t,a,b)
P(x,y)=f(1);Q(x,y)=f(2);
x1=linspace(-2*pi,2*pi,10); y1=x1;
[X,Y] = meshgrid(x1,y1);
U=P(X,Y); V=Q(X,Y);
quiver(X,Y,U,V,1.5)
hold on
t1=linspace(0,2*pi);
x=subs(r(1),t1);y=subs(r(2),t1);
plot(x,y,'r')

[Dyuman Joshi]

What are the inputs to f, r and I? Can you give a sample value?

[Pranav]

yeah, sure!

f = [(x^2) (y^2)]

r = [2*(x^2)] from (-1,2) to (2,8)

[Dyuman Joshi]

You are trying to substitute 2 values but input is only single value.

Also, (-1,2) to (2,8) is input to I?

Answer 1

[Piyush Patil]

Hello Pranav,

You are getting an error because the input vector for the 2D vector function f is not of the same size as that of the input vector for r.

In your case, f has two components, so it is a 1x2 vector, while r has only one component, so it is a scalar.

In order to resolve this error, you can rewrite the parametric curve r in terms of t only.

For example, consider the vector function f = [x^2 y^2] over the parametric curve r = [2*(t^2) 4*(t^2)] where the limits of integration for t are [-4 4]

syms x y t
f = input('Enter the components of 2D vector function [u,v]: ');
r = input('Enter x,y in parametric form [x(t),y(t)]: ');
I = input('Enter the limits of integration for t in the form [a,b]: ');
a = I(1)
b = I(2)
dr = diff(r, t)
F = subs(f, {x,y}, r)

Where your inputs are -

f = [x^2 y^2]

r = [2*(t^2) 4*(t^2)]

I = [-4 4]