The figure below represents a cube ABCDEFGH with the plane (IJK) having Cartesian equation $4x - 6y - 4z + 3 = 0$ in the orthonormal coordinate system $(\mathrm{A}; \overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{AE}})$. We denote by R the orthogonal projection of point F onto the plane (IJK). Point R is therefore the unique point of the plane (IJK) such that the line (FR) is orthogonal to the plane (IJK). We define the interior of the cube as the set of points $M(x; y; z)$ such that $\left\{\begin{array}{l} 0 < x < 1 \\ 0 < y < 1 \\ 0 < z < 1 \end{array}\right.$ Is point R inside the cube?
The figure below represents a cube ABCDEFGH with the plane (IJK) having Cartesian equation $4x - 6y - 4z + 3 = 0$ in the orthonormal coordinate system $(\mathrm{A}; \overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{AE}})$.\\
We denote by R the orthogonal projection of point F onto the plane (IJK). Point R is therefore the unique point of the plane (IJK) such that the line (FR) is orthogonal to the plane (IJK).\\
We define the interior of the cube as the set of points $M(x; y; z)$ such that $\left\{\begin{array}{l} 0 < x < 1 \\ 0 < y < 1 \\ 0 < z < 1 \end{array}\right.$\\
Is point R inside the cube?