Question

If P(6, 10, 10), Q(1, 0, -5), R(6, -10, λ) are vertices of a triangle right angled at Q, then value of λ is ______.

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Answer 1

If P(6, 10, 10), Q(1, 0, -5), R(6, -10, λ) are vertices of a triangle right angled at Q, then value of λ is 0.

Explanation:

In Δ PQR is right angled, at θ

∴ PR² = PQ² + RQ²

⇒ (6 - 6)² + (-10 - 10)² + (λ - 10)² + [(1 - 6)² + (0 + 10)² + (- 5 - λ)²]

⇒ 400 + λ² + 100 - 20λ = (25 + 100+ 225) + (25 + 100+ 25 + λ² + 10λ)

⇒ λ² - 20λ+ 500 = 350 + 150 + 10λ + λ² 

⇒ - 20λ + 10 λ

⇒ 30 λ = 0 

⇒ λ = 0