Right-hand rule and vector cross product

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Right-hand rule for vector product, with examples of the unit vectors of a cartesian coordinate system, the force due to a magnetic field, as well as the rotation vector, angular momentum vector, magnetic momentum and magnetic field due to a current.
Also see other figures under the “vectors” tag: vector sum rule, scalar production, or the divergence and curl of vector fields.

Right-hand rule for a general vector product a⨯b:

Right-handed coordinate system x̂⨯ŷ = ẑ:

Right-handed rule for the magnetic force:

Right-handed rule for the rotation vector:

Right-handed rule for the angular momentum vector:

Right-handed rule for the magnetic momentum vector:

Right-handed rule for the magnetic field lines due to a current-carrying wire:

Edit and compile if you like:

% Author: Izaak Neutelings (July 2018)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{tikz}
\usepackage{physics}
\tikzset{>=latex} % for LaTeX arrow head
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\usepackage{xcolor}
\colorlet{pinkskin}{pink!25}
\colorlet{brownskin}{pink!5!brown!45}
\colorlet{myred}{red!90!black}
\colorlet{myblue}{blue!90!black}
\colorlet{mypurple}{blue!50!red!80!black!80}
\colorlet{Bcol}{violet!90}
\colorlet{BFcol}{red!60!black}
\colorlet{veccol}{green!45!black}
\colorlet{Icol}{blue!70!black}
\colorlet{mucol}{red!90!black}
\tikzstyle{BField}=[->,line width=2,Bcol]
\tikzstyle{current}=[->,Icol] %thick,
\tikzstyle{force}=[->,line width=2,BFcol]
\tikzstyle{vector}=[->,line width=2,veccol]
\tikzstyle{thick vector}=[->,line width=2,veccol]
\tikzstyle{mu vector}=[->,line width=2,mucol]
\tikzstyle{velocity}=[->,line width=2,veccol]
\tikzstyle{charge+}=[very thin,draw=black,top color=red!50,bottom color=red!90!black,shading angle=20,circle,inner sep=0.5]
\begin{document}
\Large
% RIGHT HAND RULE F = qvxB (brown)
\begin{tikzpicture}
  \coordinate (O) at (1.2,0.3); % ORIGIN
  \coordinate (WT) at ( 2.9,-1.1); % WRIST TOP
  \coordinate (T1) at ( 2.3, 0.7); % THUMB
  \coordinate (T2) at ( 1.75, 2.3);
  \coordinate (T3) at ( 2.0, 3.1);
  \coordinate (T4) at (1.38, 3.15);
  \coordinate (T5) at ( 0.9, 2.3);
  \coordinate (T6) at ( 0.85, 1.2);
 
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Click to download: righthand_rule.tex • righthand_rule.pdf
Open in Overleaf: righthand_rule.tex

5 Replies to “Right-hand rule and vector cross product”

  1. Hello,

    Wagner again here!

    I have taken on a project to draw the left hand rule, using your code as the base.

    As soon as I have it working and I understand what I am doing, I will send you the code.

    Thank you for sharing all of this!

    Reply

    1. Hi Wagner,

      Nice, thanks! I think you can avoid some translation work if you simply add xscale=-1 to mirror the image:

      \begin{tikzpicture}[xscale=-1]
        ...
      \end{tikzpicture}
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      or

      \begin{tikzpicture}
        \begin{scope}[xscale=-1]
          % code for the hand
        \end{scope}
        % code for the arrows etc.
      \end{tikzpicture}
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      Cheers,
      Izaak

      Reply

      1. Fantastic!

        By the time that you sent this message, I had done most of the work on the left hand. I would have done it anyway, as I wanted to learn about the out and in angles, curves, looseness and all of that. It was a good exercise to have done, so that I can do other things in the future! 🙂

        I have been breaking down some of your codes and attempting to understand it line by line, at least the ones that I feel that I can expand into other areas, such as the hand and the projectile motion.

        If I do anything interesting in the future that you have not yet done, I will be sharing it with you!

        Thank you,

        Wagner.

        Reply

  2. I am a student at the Escuela Superior de Física y Matemáticas. I am currently taking Physics I, in which I am preparing my notes using LaTeX. During this process, I came across your LaTeX code to illustrate the ‘Right Hand Rule’ and would like to incorporate it into my notes.

    In order to adapt it better to my materials, I would make some modifications to the original code. However, I would like to know if it would be possible to use your drawing, making sure that I do not infringe any copyright.

    Thank you in advance for your time and attention, and I look forward to your reply.

    Sincerely,
    Vicente C. Gámez

    Reply

    1. Hi Vincente,

      Thanks for asking, but you do not need any explicit permission. All materials on this website fall under the Attribution-ShareAlike 4.0 International license. You can read more here: https://creativecommons.org/licenses/by-sa/4.0/.

      For example, you could write something like “Adopted from [link/reference to this webstite]”. I personally am not so strict about it.

      Best of luck,

      Izaak

      Reply

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