JEE Mains · Maths · STD 12 - 11. three dimension geometry
Equation of a plane at a distance \(\sqrt{\frac{2}{21}}\) from the origin, which contains the line of intersection of the planes \(x-y-z-1=0\) and \(2 x+y-3 z+4=0\) is :
- A \(3 x-y-5 z+2=0\)
- B \(3 x-4 z+3=0\)
- C \(-x+2 y+2 z-3=0\)
- D \(4 x-y-5 z+2=0\)
Answer & Solution
Correct Answer
(D) \(4 x-y-5 z+2=0\)
Step-by-step Solution
Detailed explanation
Required equation of plane \(\mathrm{P}_{1}+\lambda \mathrm{P}_{2}=0\) \((\mathrm{x}-\mathrm{y}-\mathrm{z}-1)+\lambda(2 \mathrm{x}+\mathrm{y}-3 \mathrm{z}+4)=0\) Given that its dist. From origin is \(\frac{2}{\sqrt{21}}\) Thus…
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