Image next to Equation

Question

I am trying to make my first LaTeX file and have been reading syntax for a bit and have not been able to figure one thing out yet and don't seem to find anything about it online so I thought I might just ask:)

How is it possible to place an image next to an equation?

I tried to do it by wrapping it around, putting it into a table or anything similar but I can't get it working... Of course I could just have used the syntax wrong since I'm new to the subject:) It's for a summary for my exams and the pages are limited so I would like to save some space, plus it would look a lot better.

Additionally, if anyone could give me a link to a tutorial that is a bit more extensive than just the basics i would be very thankful as well!

\documentclass[11pt, a4paper]{article}      
\usepackage{geometry}                        
\usepackage{amsmath}
\usepackage{wrapfig}
\geometry{a4paper}                                      
\usepackage{graphicx}                   
\usepackage{amssymb}
\geometry{left=5mm, right=5mm, top=0mm, bottom=5mm}

\title{\huge {\textbf{Lineare Algebra}}}
\author{ David Wright}

\date{\today}

\begin{document}
\maketitle{\large{\textbf{Vektorgeometrie}}}
\vspace {5mm}

\maketitle{\textbf{Skalarprodukt}}

Das Skalarprodukt ergibt die L\"{a}nge der Projektion von \ensuremath{\vec{a}} auf \ensuremath{\vec{b}}.


\begin {tabular}{p{10cm}l}
{\begin {align*}
\vec{a} \bullet \vec{b}& = |\vec{a}| \cdot |\vec{b}| \cdot \cos(\phi) \\
                       & = a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z \\
            \cos(\phi) & =  \frac {\vec{a} \bullet \vec{b}}{|\vec{a}| \cdot  |\vec{b}|}\\
                       & = \frac {a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z}{\sqrt{a_x^2 + a_y2 + a_z^2}\sqrt{b_x^2 + b_y^2 + b_z^2}}
\end {align*}}
&

\includegraphics[keepaspectratio = true, scale = 1] {dotp.jpg}
\end{tabular}

\vspace{5mm}

\maketitle{\textbf{Vektorprodukt}}

TextTextTextTextTextTextTextTextTextText


\end{document}  

Answer 1

There are several possibilities. Perhaps the simplest is

\usepackage{graphicx}

...

\begin{tabular}{p{3cm}c}
\begin{equation}
1=1
\end{equation}
&
\includegraphics{mypic}
\end{tabular}

or with align:

\documentclass{article}

\usepackage{graphicx,amsmath}

\begin{document}

\begin{tabular}{p{5cm}c}
{\begin{align}
1&=1\\
11&=22
\end{align}}
&
\includegraphics[draft]{mypic}
\end{tabular}

\end{document}

Answer 2

Instead of using a tabularenvironment to position the objects, there is also the possibility to make the graphics part of the math formula, for example like this:

\[
\begin {aligned}
\vec{a} \bullet \vec{b}& = |\vec{a}| \cdot |\vec{b}| \cdot \cos(\phi) \\
                       & = a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z \\
            \cos(\phi) & =  \frac {\vec{a} \bullet \vec{b}}{|\vec{a}| \cdot  |\vec{b}|}\\
                       & = \frac {a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z}{\sqrt{a_x^2 + a_y2 + a_z^2}\sqrt{b_x^2 + b_y^2 + b_z^2}}
\end {aligned}
\qquad
\raisebox{-15mm}{\includegraphics[keepaspectratio = true, scale = 1] {dotp.jpg}}
\]

The \qquad is used to get some whitespace (2em) and \raisebox is only there is you have to adjust the picture vertically.

Answer 3

I recommend using "subcaption" package. Look at this link for the manual of the package. (link: click here)

I didn't have your dotp.jpg file so I just took a screenshot, copy-pasted in paint and cut a part of the screensot and saved it in a png file. So sorry for the quality in the image I uploaded below the code I wrote for you here.

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{subcaption}
\author{AmirHosein Sadeghimanesh}
\title{Equation-and-image-side-by-side-20200202}
\begin{document}
    \maketitle

    \begin{figure}[h]
        \centering
        \begin{subfigure}[b]{0.45\textwidth}
            \centering
            \begin {align*}
            \vec{a} \bullet \vec{b}& = |\vec{a}| \cdot |\vec{b}| \cdot \cos(\phi) \\
            & = a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z \\
            \cos(\phi) & =  \frac {\vec{a} \bullet \vec{b}}{|\vec{a}| \cdot  |\vec{b}|}\\
            & = \frac {a_x  \cdot b_x + a_y \cdot b_y + a_z \cdot b_z}{\sqrt{a_x^2 + a_y2 + a_z^2}\sqrt{b_x^2 + b_y^2 + b_z^2}}
            \end {align*}
            \caption{Equation.}
            \label{fig:equation}
        \end{subfigure}
        \hfill
        \begin{subfigure}[b]{0.45\textwidth}
            \centering
            \includegraphics[width=\textwidth]{dotp.png}
            \caption{Image.}
            \label{fig:image}
        \end{subfigure}
        \caption{Total caption.}
    \end{figure}