# Multi align equation right

I am trying to obtain the following alignment for my three equation

The best I have been able to do is the following

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage[latin1]{inputenc}

\begin{document}
\maketitle

\begin{align*}
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{align*}
\end{document}


However this leaves huge whitespaces in the equation.

\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.

You can also use an array for this.

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}

\newcommand{\ii}{\mathbf{\,i}}
\newcommand{\jj}{\mathbf{\,j}}

$\begin{array}{r @{{}={}} r @{} r} \mathbf{r}(\theta) & (x_0 + a \cos x) \ii +{} & (y_0 + a \sin x) \jj \\ \mathbf{r}'(\theta) & - a \sin x \ii +{} & (a \cos x) \jj \\ \mathbf{F}(\mathbf{r}(\theta)) & 0 \ii +{} & (x_0 + a \sin x) \jj \end{array}$

\end{document}