In space, with respect to an orthonormal coordinate system, we consider the points $\mathrm { A } ( 1 ; - 1 ; - 1 )$, $\mathrm { B } ( 1 ; 1 ; 1 ) , \mathrm { C } ( 0 ; 3 ; 1 )$ and the plane $\mathscr { P }$ with equation $2 x + y - z + 5 = 0$. Let $\mathscr { D } _ { 1 }$ be the line with direction vector $\vec { u } ( 2 ; - 1 ; 1 )$ passing through A. A parametric representation of the line $\mathscr { D } _ { 1 }$ is : a. $\left\{ \begin{array} { l } x = 2 + t \\ y = - 1 - t \\ z = 1 - t \end{array} \quad ( t \in \mathbb { R } ) \right.$ b. $\left\{ \begin{array} { l } x = - 1 + 2 t \\ y = 1 - t \\ z = 1 + t \end{array} \quad ( t \in \mathbb { R } ) \right.$ c. $\left\{ \begin{array} { l } x = 5 + 4 t \\ y = - 3 - 2 t \\ z = 1 + 2 t \end{array} \quad ( t \in \mathbb { R } ) \right.$ d. $\left\{ \begin{array} { l } x = 4 - 2 t \\ y = - 2 + t \\ z = 3 - 4 t \end{array} \quad ( t \in \mathbb { R } ) \right.$
In space, with respect to an orthonormal coordinate system, we consider the points $\mathrm { A } ( 1 ; - 1 ; - 1 )$, $\mathrm { B } ( 1 ; 1 ; 1 ) , \mathrm { C } ( 0 ; 3 ; 1 )$ and the plane $\mathscr { P }$ with equation $2 x + y - z + 5 = 0$.
Let $\mathscr { D } _ { 1 }$ be the line with direction vector $\vec { u } ( 2 ; - 1 ; 1 )$ passing through A.\\
A parametric representation of the line $\mathscr { D } _ { 1 }$ is :\\
a. $\left\{ \begin{array} { l } x = 2 + t \\ y = - 1 - t \\ z = 1 - t \end{array} \quad ( t \in \mathbb { R } ) \right.$\\
b. $\left\{ \begin{array} { l } x = - 1 + 2 t \\ y = 1 - t \\ z = 1 + t \end{array} \quad ( t \in \mathbb { R } ) \right.$\\
c. $\left\{ \begin{array} { l } x = 5 + 4 t \\ y = - 3 - 2 t \\ z = 1 + 2 t \end{array} \quad ( t \in \mathbb { R } ) \right.$\\
d. $\left\{ \begin{array} { l } x = 4 - 2 t \\ y = - 2 + t \\ z = 3 - 4 t \end{array} \quad ( t \in \mathbb { R } ) \right.$