Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

The origin side of $2y-z+2=0$ (value $2>0$ at the origin) requires $2\lambda -1+2>0$, so $\lambda >-\frac{1}{2}$. The origin side of $2y+3z-6=0$ (value $-6<0$ at the origin) requires $2\lambda +3-6<0$, so $\lambda <\frac{3}{2}$. Hence $\lambda \in \left(-\frac{1}{2},\frac{3}{2}\right)$.