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Punctul 5 de la primul subiect,

Punctul 5 De La Primul Subiect class=

Răspuns :

[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]