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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Equation of the plane passing through A (x₁, y₁, z₁ ) and containing the line x-x₂ d₁ = y-y₂ d₂ = z-z₂ d₃ is

Options

  1. A| array ccc x-x₁ & y-y₁ & z-z₁ x₂-x₁ & y₂-y₁ & z₂-z₁ d₁ & d₂ & d₃ array |=0
  2. B| array ccc x-x₂ & y-y₂ & z-z₂ x₁-x₂ & y₁-y₂ & z₁-z₂ d₁ & d₂ & d₃ array |=0
  3. C| array ccc x - d ₁ & y - d ₂ & z - d ₃ x ₁ & y ₁ & z ₁ x ₂ & y ₂ & z ₂ array |=0
  4. D| array ccc x & y & z x₁-x₂ & y₁-y₂ & z₁-z₂ d₁ & d₂ & d₃ array |=0

Correct answer

B. | array ccc x-x₂ & y-y₂ & z-z₂ x₁-x₂ & y₁-y₂ & z₁-z₂ d₁ & d₂ & d₃ array |=0

Step-by-step solution

Vectors A R , A B & C are coplanar Equation of the required plane | array ccc x-x₁ & y-y₁ & z-z₁ x₂-x₁ & y₂-y₁ & z₂-z₁ d₁ & d₂ & d₃ array |=0 or | array ccc x-x₂ & y-y₂ & z-z₂ x₁-x₂ & y₁-y₂ & z₁-z₂ d₁ & d₂ & d₃ array |=0

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