Question

The plane 2x − (1 + λ) y + 3λz = 0 passes through the intersection of the planes

Options

• 2x − y = 0 and y − 3z = 0

• 2x + 3z = 0 and y = 0

• 2x − y + 3z = 0 and y − 3z = 0

• None of these

Answer 1

 2x − y = 0 and y − 3z = 0

\[\text{ The given plane is } \]

\[2x - \left( 1 + \lambda \right) y + 3\lambda z = 0\]

\[ \Rightarrow \left( 2x - y \right) + \lambda \left( - y + 3z \right) = 0\]

\[\text{ So, this plane passes through the intersection of the planes } \]

\[2x - y = 0 \text{ and }  - y + 3z = 0\]

\[ \Rightarrow 2x - y = 0 \text{ and } y - 3z = 0\]