trong k gian với hệ tọa độ Oxyz cho (P) : 2x-y+2=0 và d(m) là giao (A) : (2m+1)x-(m-1)y+m-1=0 ; (B) : mx +(2m+1)z +4m +2 =0 ( M là tham số ) xác định m để d(m) song song với (P)$$
$d(m)$ có vetor chỉ phương $\overrightarrow{u_m}=[\overrightarrow{n_A};\overrightarrow{n_B}]=((1-m)(2m+1);-(2m+1)^2;m(1-m))$
$d(m)//(P)\Rightarrow \overrightarrow{u_m}$ vuông góc $\overrightarrow{n_{(P)}} \Rightarrow \overrightarrow{u_m}.\overrightarrow{n_{(P)}}=0$ 
$\Leftrightarrow \begin{cases}\begin{matrix} -2(m-1)(2m+1)=0\\ 1.(2m+1)^2=0 \end{matrix} \\ 0=0 \end{cases}\Leftrightarrow m=\frac{-1}{2}$ 

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