JEE Mains · Maths · STD 12 - 11. three dimension geometry
The equation of a plane containing the line of intersection of the planes \(2x - y - 4 = 0\) and \(y + 2z - 4 = 0\) and passing through the point \((1, 1, 0)\) is
- A \(x + 3y + z = 4\)
- B \(2x - z = 2\)
- C \(x - 3y - 2z = -2\)
- D \(x - y - z = 0\)
Answer & Solution
Correct Answer
(D) \(x - y - z = 0\)
Step-by-step Solution
Detailed explanation
The required plane is \((2 x-y-4)+\lambda(y+2 z-4)=0\) it passes through \((1,1,0)\) \(\Rightarrow(2-1-4)+\lambda(1-4)=0\) \(\Rightarrow-3-3 \lambda=0 \Rightarrow \lambda=-1\) \(\Rightarrow x-y-z=0\)
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