In the orthonormal frame $(A ; \overrightarrow{AB} ; \overrightarrow{AD} ; \overrightarrow{AE})$, $ABCDEFGH$ denotes a cube with side length 1. $\mathscr{P}$ denotes the plane $(AFH)$. In the orthonormal frame $(A ; \overrightarrow{AB} ; \overrightarrow{AD} ; \overrightarrow{AE})$: a. Plane $\mathscr{P}$ has Cartesian equation: $x + y + z - 1 = 0$. b. Plane $\mathscr{P}$ has Cartesian equation: $x - y + z = 0$. c. Plane $\mathscr{P}$ has Cartesian equation: $-x + y + z = 0$. d. Plane $\mathscr{P}$ has Cartesian equation: $x + y - z = 0$.
In the orthonormal frame $(A ; \overrightarrow{AB} ; \overrightarrow{AD} ; \overrightarrow{AE})$, $ABCDEFGH$ denotes a cube with side length 1. $\mathscr{P}$ denotes the plane $(AFH)$.
In the orthonormal frame $(A ; \overrightarrow{AB} ; \overrightarrow{AD} ; \overrightarrow{AE})$:\\
a. Plane $\mathscr{P}$ has Cartesian equation: $x + y + z - 1 = 0$.\\
b. Plane $\mathscr{P}$ has Cartesian equation: $x - y + z = 0$.\\
c. Plane $\mathscr{P}$ has Cartesian equation: $-x + y + z = 0$.\\
d. Plane $\mathscr{P}$ has Cartesian equation: $x + y - z = 0$.