JEE Mains · Maths · STD 12 - 11. three dimension geometry
If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \(2 x+4 y+5 z=8\) and \(3 x-2 y+3 z=5\) is \(\alpha x+\beta y+\gamma z+97=0\) then \(\alpha+\beta+\gamma=...........\).
- A \(18\)
- B \(17\)
- C \(16\)
- D \(15\)
Answer & Solution
Correct Answer
(D) \(15\)
Step-by-step Solution
Detailed explanation
The equation of plane through \((-2,3,5)\) is \(a(x+2)+b(y-3)+c(z-5)=0\) it is perpendicular to \(2 x+4 y+5 z=8\) and \(3 x-2 y+3 z=5\) \(2 a+4 b+5 c=0\) \(3 a-2 b+3 c=0\)…
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