यदि बिंदु (1, 3, -2), (2, λ, 1) और (3, 4, -1) एक-दूसरे के समतलीय हैं, तो λ का मान क्या है?

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1
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Agniveer Navy SSR Full Test - 01
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Detailed Solution

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संकल्पना:

बिंदु (x1, y1, z1), (x2, y2, z2) और (x3, y3, z3) के समतलीय होने के लिए

गणना:

दिए गए बिंदु (1, 3, -2), (2, λ, 1) और (3, 4, -1) हैं। 

तल का समीकरण निम्न होगा

⇒ 1(-λ - 4) - 3(-2 - 3) + (-2)(8 - 3λ) = 0

⇒ 5λ - 4 + 15 - 16 = 0

⇒ 5λ = 5

⇒ λ = 1

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