Question

The plane 2x − (1 + λ) y + 3λz = 0 passes through the intersection of the planes
(a) 2x − y = 0 and y − 3z = 0
(b) 2x + 3z = 0 and y = 0
(c) 2x − y + 3z = 0 and y − 3z = 0
(d) None of these

Answer 1

(a) 2x − y = 0 and y − 3z = 0

$$\begin{gathered} \text{The given plane is} \\ 2x-\left(1+\lambda \right)y+3\lambda z=0 \\ \Rightarrow \left(2x-y\right)+\lambda \left(-y+3z\right)=0 \\ \text{So, this plane passes through the intersection of the planes} \\ 2x-y=0\text{and}-y+3z=0 \\ \Rightarrow 2x-y=0\text{and}y-3z=0 \end{gathered}$$