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 $2 x + y - z + 5 = 0$. a. The intersection of the plane $\mathscr { P }$ and the plane $( \mathrm { ABC } )$ is reduced to a single point. b. The plane $\mathscr { P }$ and the plane ( ABC ) are identical. c. The plane $\mathscr { P }$ intersects the plane $( \mathrm { ABC } )$ along a line. d. The plane $\mathscr { P }$ and the plane ( ABC ) are strictly parallel.
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 $2 x + y - z + 5 = 0$.
a. The intersection of the plane $\mathscr { P }$ and the plane $( \mathrm { ABC } )$ is reduced to a single point.\\
b. The plane $\mathscr { P }$ and the plane ( ABC ) are identical.\\
c. The plane $\mathscr { P }$ intersects the plane $( \mathrm { ABC } )$ along a line.\\
d. The plane $\mathscr { P }$ and the plane ( ABC ) are strictly parallel.