[tex]5)xOy[/tex]
[tex]A(1,1),B(3,2),C(m,3)[/tex]
[tex]A(x_{A},y_{A}),B(x_{B},y_{B}),C(x_{C},y_{C})[/tex]
[tex]m=? \: \: \: ,m\:\in\:\mathbb{R} \: stiind\:ca\:A,B,C\:coliniare[/tex]
A,B,C coliniare dacă :
[tex]\begin{vmatrix}
x_{A}& y_{A} & 1\\
x_{B}& y_{B} & 1\\
x_{C}& y_{C} & 1
\end{vmatrix} = 0[/tex]
[tex]\begin{vmatrix}
1& 1& 1\\
3& 2& 1\\
m& 3 & 1
\end{vmatrix} = 0[/tex]
[tex]1 \times 2 \times 1 + 3 \times 3 \times 1 + m \times 1 \times 1 - 1 \times 2 \times m - 1 \times 3 \times 1 - 1 \times 1 \times 3 = 0 [/tex]
[tex]2 + 9 + m - 2m - 3 - 3 = 0 [/tex]
[tex] - m = 5 \: | \times ( - 1)[/tex]
[tex]m = - 5 \: \in \: \mathbb{R}[/tex]
