\title{Relación lineal}
\language{en}
\range{-5..5}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{no}
\format{html}
\precision{1000000}

\integer{c11=random(2..10)*random(-1,1)}
\integer{c12=random(2..10)*random(-1,1)}
\integer{c13=random(2..10)*random(-1,1)}
\integer{c21=random(2..10)*random(-1,1)}
\integer{c22=random(2..10)*random(-1,1)}
\integer{c23=random(2..10)*random(-1,1)}

\statement{Sean los 3 vectores del plano:
<p><center>
 v<sub>1</sub> = (\c11,\c21) ,
 v<sub>2</sub> = (\c12,\c22) ,
 v<sub>3</sub> = (\c13,\c23) ,
</center> <p>

Hallar 3 enteros a,b,c tales que
<p><center>
	a v<sub>1</sub> + b v<sub>2</sub> + c v<sub>3</sub> = 0 ,
</center> <p>
siendo los números a,b,c no todos cero.
}

\answer{a}{\sx}
\answer{b}{\sy}
\answer{c}{\sz}

\condition{a,b,c son enteros y no todos cero}
{
abs(\sx)+abs(\sy)+abs(\sz)>0 and
abs(round(\sx)-(\sx))<=0 and
abs(round(\sy)-(\sy))<=0 and
abs(round(\sz)-(\sz))<=0
}

\condition{La suma algebráica de los vectores es cero}
{
(\c11)*(\sx)+(\c12)*(\sy)+(\c13)*(\sz)=0 y
(\c21)*(\sx)+(\c22)*(\sy)+(\c23)*(\sz)=0
}