Mathematics - Determinant Question with Solution | TestHub
MathematicsDeterminantApplication of det. In geometryMedium3 minQB
MathematicsMediuminteger
Passage / Comprehension
Let λ 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 area of the triangle (in sq. units) is equal to
Answer:
3
Solution:
Points of concurrency: λ = −2 gives P₁ = (0, 1); λ = −1 gives P₂ = (−1, 0); λ = 2 gives P₃ = (2, −3). Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| = ½|0 + 4 + 2| = 3. Answer: 3
Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:Application of det. In geometry
⏱ 3mℹ️ Source: QB
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