Multi align equation right
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage[latin1]{inputenc}% really? that is very 20th century, why not utf8?
\begin{document}
\begin{alignat*}{3}
r(\theta) ={}&& (x_0 + a \cos x) i + {}&& (y_0 + a \sin x) j \\
r'(\theta) ={}&& - a \sin x i + {}&& (a \cos x) j \\
F(r(\theta)) ={}&& 0 i + {}&& (x_0 + a \sin x) j
\end{alignat*}
\end{document}
alignat
is a variant of align
that avoids adding extra space. You need &&
so you only use the right aligned columns not the left aligned, and then you need {}
after the =
and +
to preserve the correct spacing as they are before the &
not after.