Mathematics - Determinant Question with Solution | TestHub
MathematicsDeterminantApplication of det. In geometryMedium3 minQB
MathematicsMediuminteger
Passage / Comprehension
Let be a real parameter and consider the three straight lines L₁: λx + y − 1 = 0, L₂: 2x + λy + 2 = 0, L₃: y + λ + 1 = 0. For certain real values of λ the three lines are concurrent. Let λ₁ < λ₂ < λ₃ denote all real values of λ for which L₁, L₂, L₃ are concurrent, and let P₁, P₂, P₃ be the corresponding points of concurrency.
The product is equal to
Answer:
4
Solution:
For concurrency, the coefficient determinant vanishes: |λ 1 −1; 2 λ 2; 0 1 λ+1| = λ³ + λ² − 4λ − 4 = (λ+1)(λ+2)(λ−2) = 0. Hence λ₁ = −2, λ₂ = −1, λ₃ = 2, and the product λ₁λ₂λ₃ = (−2)(−1)(2) = 4. Answer: 4
Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:Application of det. In geometry
⏱ 3mℹ️ Source: QB
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