Trong không gian Oxyz, cho hai vectơ u= (m; -2; m+1) và v = (3; -2m; 6). Tìm tham số m để hai vectơ đã cho cùng phương.

Đáp án đúng là: B

Để hai vectơ đã cho cùng phương thì $\overrightarrow{u}=k.\overrightarrow{v},\left(k\in \mathbb{Z},\text{\hspace{0.33em}}k\ne 0\right)$

$\Rightarrow \left(m;-2;m+1\right)=k.\left(3;-2m-4;6\right)$

$\Rightarrow \left\{\begin{array}{c}m=3k\\ -2=-2mk-4k\\ m+1=6k\end{array}\right.\iff \left\{\begin{array}{c}m-3k=0\\ mk+2k=1\\ m-6k=-1\end{array}\right.$

$\iff \left\{\begin{array}{c}m-3k=0\\ mk+2k=1\\ 3k=1\end{array}\right.\iff \left\{\begin{array}{c}m-3k=0\\ mk+2k=1\\ k=\frac{1}{3}\end{array}\right.$

$\iff \left\{\begin{array}{c}m=1\\ m+2=3\\ k=\frac{1}{3}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\end{array}\right.\iff \left\{\begin{array}{c}m=1\\ k=\frac{1}{3}\end{array}\right.$(Thỏa mãn)