1 \section{The object \texttt{vecteur}}
3 \subsection{Definition with components}
5 The object \Lkeyword{vecteur} allows us to define a \Index{vector}. The simplest way to do
6 that is to use the argument \texttt{\Lkeyword{args}=$x$ $y$ $z$} to specify its \Index{components}.
8 \psset{lightsrc=10 -20 50,viewpoint=50 -20 30 rtp2xyz,Decran=100}
9 \begin{LTXexample}[width=6cm]
10 \begin{pspicture*}(-1,-1)(1,2)
11 \psSolid[object=vecteur,
15 \psSolid[object=vecteur,
18 \psSolid[object=vecteur,
20 linecolor=blue](1,0,0)
24 \subsection{Definition with 2 points}
26 We can also define a vector with 2 given points $A$ and $B$ of $\mathbb{R}^3$.
28 We then use the arguments \texttt{\Lkeyword{definition}=\Lkeyval{vecteur3d}} and \texttt{\Lkeyword{args}=$x_A$ $y_A$ $z_A$ $x_B$
29 $y_B$ $z_B$} where $(x_A, y_A, z_A)$ and $(x_B, y_B, z_B)$ are the appropriate coordinates of the points $A$ and $B$
31 If the points $A$ and $B$ were already defined, we can easily use the named variables:
32 \texttt{\Lkeyword{args}=$A$ $B$}.
34 \psset{lightsrc=10 -20 50,viewpoint=20 20 20,Decran=20}
35 \begin{LTXexample}[width=6cm]
36 \begin{pspicture*}(-3,-3)(4.5,2)
44 \psSolid[object=vecteur,
51 \subsection{Some other definitions of a vector}
53 There are some other possibilities to define a \Index{vector}. Here a list of some
54 possible definitions with the appropriate arguments:
58 \item \texttt{\Lkeyword{definition}=\Lkeyval{addv3d}};
59 \texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
61 Addition of 2 vectors.
63 \item \texttt{\Lkeyword{definition}=\Lkeyval{subv3d}};
64 \texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
66 Difference of 2 vectors.
68 \item \texttt{\Lkeyword{definition}=\Lkeyval{mulv3d}};
69 \texttt{\Lkeyword{args}= $\vec u$ $\lambda $}.
71 \Index{Multiplication} of a vector with a real.
73 \item \texttt{\Lkeyword{definition}=\Lkeyval{vectprod3d}};
74 \texttt{\Lkeyword{args}= $\vec u$ $\vec v$}.
76 \Index{Vector product} of 2 vectors.
78 \item \texttt{\Lkeyword{definition}=\Lkeyval{normalize3d}};
79 \texttt{\Lkeyword{args}= $\vec u$}.
81 \Index{Normalized vector} $\Vert \vec u\Vert ^{-1} \vec u$.