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