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From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)
- a)
- b)1
- c)-1
- d)
Correct answer is option 'C'. Can you explain this answer?
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From a point P(λ, λ, λ), perpendicular PQ and PR ...
Lines are x = y, z = 1
Let Q (a, a, 1) and R (– β,β, – 1) Direction ratios of PQ are λ – α, λ – α, λ – 1 and direction ratios of PR are λ + β, λ – β, λ + 1
∴ PQ is perpendicular to line (1)
∴ PQ is perpendicular to line (1)
∴ – (λ + β) + λ – β = 0 ⇒ b = 0
∴ dr’s of PQ are 0, 0, λ – 1 and dr’s of PR are λ, λ, λ + 1
∵ ∠QPR = 90° ⇒ (λ – l) (λ + 1) = 0 ⇒ λ = 1 or – 1
But for λ = 1, we get point Q itself
∴ we take λ = – 1
∴ dr’s of PQ are 0, 0, λ – 1 and dr’s of PR are λ, λ, λ + 1
∵ ∠QPR = 90° ⇒ (λ – l) (λ + 1) = 0 ⇒ λ = 1 or – 1
But for λ = 1, we get point Q itself
∴ we take λ = – 1
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From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option 'C'. Can you explain this answer?
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From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option '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 From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option '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 From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option 'C'. Can you explain this answer?.
From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option '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 From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option '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 From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)a)b)1c)-1d)Correct answer is option 'C'. Can you explain this answer?.
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