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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Equation of the plane passing through the line of intersection of the two planes r n ₁=q₁ and r n ₂=q₂ and parallel to the line of intersection of r n ₃=q₃ and r n ₄=q₄ is

Options

  1. Adependent on n ₁ n ₃
  2. Bdependent on n ₃ n ₄
  3. Cindependent of q ₁ and q ₂
  4. Dindependent of q ₃ and q ₄

Correct answer

D. independent of q ₃ and q ₄

Step-by-step solution

Equation of the required plane is ( r n ₁ - q ₁ )+ ( r n ₂ - q ₂ )=0 r ( n ₁ + n ₂ )= ( q ₁+ q ₂ ) Now, perpendicular to n ₃ n ₄⁻ aligned & ( n ₁+ n ₂ ) ( n ₃ n ₄ )=0 & =- [ n ₁ n ₃ n ₄ ] [ n ₂ n ₃ n ₄ ] aligned So independent on q ₃ and q ₄ only.

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