Cho mặt phẳng \[\left( P \right):x - 2y + mz = 0\] và đường thẳng \[d:\frac{{x - 1}}{2} = \frac{{y + 1}}{{ - 4}} = \frac{{z - 3}}{1}\]. Tìm tham số \[m\] để \[d \bot \left( P \right)\].

A. \[\left\{ \begin{array}{l}x = 2 + 2t\\y = - t\\z = - 1 + t\end{array} \right.{\rm{ }}\left( {t \in \mathbb{R}} \right).\]

B. \[\left\{ \begin{array}{l}x = 2 + 2t\\y = - t\\z = - 1 - t\end{array} \right.{\rm{ }}\left( {t \in \mathbb{R}} \right).\]

C. \[\left\{ \begin{array}{l}x = 2 + 2t\\y = - 1\\z = - 1 + t\end{array} \right.{\rm{ }}\left( {t \in \mathbb{R}} \right).\]

D. \[\left\{ \begin{array}{l}x = 2 + 2t\\y = - t\\z = 1 - t\end{array} \right.{\rm{ }}\left( {t \in \mathbb{R}} \right).\]

A. 1.

B. 0.

C. 2.

D. −1.

A. \[M\left( {1; - 4;2} \right).\]

B. \[N\left( {1; - 4; - 2} \right).\]

C. \[P\left( {1;2;7} \right).\]

D. \[Q\left( {2; - 2;7} \right).\]

A. \[30^\circ.\]

B. \[90^\circ.\]

C. \[60^\circ.\]

D. \[45^\circ.\]

A. \[d \subset \left( P \right).\]

B. \[d\parallel \left( P \right).\]

C. \[d \bot \left( P \right).\]

D. \[d\] cắt \[\left( P \right).\]

A. \[\left\{ \begin{array}{l}x = 1 + 3t\\y = 3t\\z = 1 - t.\end{array} \right.\]

B. \[\left\{ \begin{array}{l}x = 1 + t\\y = 3t\\z = 1 - t.\end{array} \right.\]

C. \[\left\{ \begin{array}{l}x = 1 + 3t\\y = 1 + 3t\\z = 1 - t.\end{array} \right.\]

D. \[\left\{ \begin{array}{l}x = 1 + 3t\\y = 3t\\z = 1 + t.\end{array} \right.\]

A. \[\frac{{x - 3}}{1} = \frac{{y + 3}}{2} = \frac{{z + 2}}{2}.\]

B. \[\frac{{x + 3}}{3} = \frac{{y - 3}}{1} = \frac{{z + 2}}{{ - 2}}.\]

C. \[\frac{{x - 3}}{{ - 1}} = \frac{{y + 3}}{{ - 3}} = \frac{{z - 2}}{2}.\]

D. \[\frac{{x + 1}}{3} = \frac{{y - 3}}{{ - 3}} = \frac{{z + 5}}{2}.\]