Let \(\vec A\) be a vector defined as \(\vec A=\) -yî  + xĵ in the x-y plane. Evaluate \(\mathop \oint \limits_c \vec A.\overrightarrow {dr}\) in the x-y plane where c is an ellipse \(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1\)