JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the image of the point \(P (1,2,6)\) in the plane passing through the points \(A (1,2,0), B (1,4,1)\) and \(C(0,5,1)\) be \(Q(\alpha, \beta, \gamma)\). Then \(\left(\alpha^2+\beta^2+\gamma^2\right)\) is equal to :
- A \(65\)
- B \(70\)
- C \(76\)
- D \(62\)
Answer & Solution
Correct Answer
(A) \(65\)
Step-by-step Solution
Detailed explanation
Equation of plane \(A ( x -1)+ B ( y -2)+C(z-0)=0\) Put \((1,4,1) \Rightarrow 2 B + C =0\) Put \((0,5,1) \Rightarrow-A+3 B+C=0\) Sub : \(B - A =0 \Rightarrow A = B , C =-2 B\) \(1(x-1)+1(y-2)-2(z-0)=0\) \(x+y-2 z-3=0\) Image is \((\alpha, \beta, \gamma) pt \equiv(1,2,6)\)…
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