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Let α, β, γ, δ be real numbers such that α2 + β2 + γ2 ≠ 0 and α + β = 1. Suppose the point (3, 2, −1) is the mirror image of the point (1, 0, −1) with respect to the plane ax + βy + γz = δ. Then which of the following statements is/are TRUE? 
  • a)
    α + β = 2      
  • b)
    δ – γ = 3  
  • c)
    δ + β = 4      
  • d)
    α + β + γ = δ
Correct answer is option 'A,B,C'. Can you explain this answer?
Verified Answer
Let α, β, γ, δbe real numbers such that α...

R is mid point of PQ
∴ R(2,1,-1) and it lies on plane equation of plane is αa + βy + γz = δ
∴ 2α + β - γ = δ  ...(1) 
 Normal vector to plane is 

and α + γ = 1 (given)  ...(3)  
from (2) and (3)
∴ a = 1, β = 1, γ = 0
and from (1)  
2(1) + 1 – 0 = δ
δ = 3 
 Now :  
α + β = 2 
δ – γ = 3 
δ + β = 4 
 so, A,B,C are correct. 
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Let α, β, γ, δbe real numbers such that α...
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Let α, β, γ, δbe real numbers such that α2 + β2 + γ2 ≠ 0 and α + β = 1. Suppose the point (3, 2, −1) is the mirror image of the point (1, 0, −1) with respect to the plane ax + βy + γz= δ. Then which of the following statements is/are TRUE?a)α+ β= 2 b)δ– γ= 3c)δ+ β= 4 d)α+ β + γ=δCorrect answer is option 'A,B,C'. Can you explain this answer?
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Let α, β, γ, δbe real numbers such that α2 + β2 + γ2 ≠ 0 and α + β = 1. Suppose the point (3, 2, −1) is the mirror image of the point (1, 0, −1) with respect to the plane ax + βy + γz= δ. Then which of the following statements is/are TRUE?a)α+ β= 2 b)δ– γ= 3c)δ+ β= 4 d)α+ β + γ=δCorrect answer is option 'A,B,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let α, β, γ, δbe real numbers such that α2 + β2 + γ2 ≠ 0 and α + β = 1. Suppose the point (3, 2, −1) is the mirror image of the point (1, 0, −1) with respect to the plane ax + βy + γz= δ. Then which of the following statements is/are TRUE?a)α+ β= 2 b)δ– γ= 3c)δ+ β= 4 d)α+ β + γ=δCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let α, β, γ, δbe real numbers such that α2 + β2 + γ2 ≠ 0 and α + β = 1. Suppose the point (3, 2, −1) is the mirror image of the point (1, 0, −1) with respect to the plane ax + βy + γz= δ. Then which of the following statements is/are TRUE?a)α+ β= 2 b)δ– γ= 3c)δ+ β= 4 d)α+ β + γ=δCorrect answer is option 'A,B,C'. Can you explain this answer?.
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