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\section{The object \texttt{vecteur}}
\subsection{Definition with components}
The object \Lkeyword{vecteur} allows us to define a \Index{vector}. The simplest way to do
that is to use the argument \texttt{\Lkeyword{args}=$x$ $y$ $z$} to specify its \Index{components}.
\psset{lightsrc=10 -20 50,viewpoint=50 -20 30 rtp2xyz,Decran=100}
\begin{LTXexample}[width=6cm]
\begin{pspicture*}(-1,-1)(1,2)
\psSolid[object=vecteur,
action=draw*,
args=0 0 1,
linecolor=yellow]%
\psSolid[object=vecteur,
args=1 0 0,
linecolor=red]
\psSolid[object=vecteur,
args=0 0 1,
linecolor=blue](1,0,0)
\end{pspicture*}
\end{LTXexample}
\subsection{Definition with 2 points}
We can also define a vector with 2 given points $A$ and $B$ of $\mathbb{R}^3$.
We then use the arguments \texttt{\Lkeyword{definition}=\Lkeyval{vecteur3d}} and \texttt{\Lkeyword{args}=$x_A$ $y_A$ $z_A$ $x_B$
$y_B$ $z_B$} where $(x_A, y_A, z_A)$ and $(x_B, y_B, z_B)$ are the appropriate coordinates of the points $A$ and $B$
If the points $A$ and $B$ were already defined, we can easily use the named variables:
\texttt{\Lkeyword{args}=$A$ $B$}.
\psset{lightsrc=10 -20 50,viewpoint=20 20 20,Decran=20}
\begin{LTXexample}[width=6cm]
\begin{pspicture*}(-3,-3)(4.5,2)
\psSolid[object=plan,
linecolor=gray,
definition=equation,
args={[0 1 1 0]},
base=-1 3 -2 2,
planmarks,
plangrid]
\psSolid[object=vecteur,
definition=vecteur3d,
args=0 0 1 1 1 1]%
\end{pspicture*}
\end{LTXexample}
\subsection{Some other definitions of a vector}
There are some other possibilities to define a \Index{vector}. Here a list of some
possible definitions with the appropriate arguments:
\begin{itemize}
\item \texttt{\Lkeyword{definition}=\Lkeyval{addv3d}};
\texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
Addition of 2 vectors.
\item \texttt{\Lkeyword{definition}=\Lkeyval{subv3d}};
\texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
Difference of 2 vectors.
\item \texttt{\Lkeyword{definition}=\Lkeyval{mulv3d}};
\texttt{\Lkeyword{args}= $\vec u$ $\lambda $}.
\Index{Multiplication} of a vector with a real.
\item \texttt{\Lkeyword{definition}=\Lkeyval{vectprod3d}};
\texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
\Index{Vector product} of 2 vectors.
\item \texttt{\Lkeyword{definition}=\Lkeyval{normalize3d}};
\texttt{\Lkeyword{args}= $\vec u$}.
\Index{Normalized vector} $\Vert \vec u\Vert ^{-1} \vec u$.
\end{itemize}
\endinput
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