Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

The correct statement(s) is/are -

Options

AThe line of intersection of planes r n ₁= q ₁, r n ₂= q ₂ and r . n ₃= q ₃, r n ₄= q ₄ are perpendicular if (
BIf three distinct planes r . n ₁=q₁, r . n ₂=q₂, r . n ₃= q ₃ intersect in a line which is contained by the pl
CIf four distinct planes r n ₁= q ₁, r . n ₂= q ₂, r . n ₃= q ₃ and r n ₄= q ₄ intersect in a line, then [ arra
DIf a plane contains line of intersection of planes r n ₁= q ₁, r n ₂= q ₂ and is parallel to line of intersect

Correct answer

D. If a plane contains line of intersection of planes r n ₁= q ₁, r n ₂= q ₂ and is parallel to line of intersect

Step-by-step solution

(A) Line of intersection of r n ₁= q ₁ & r n ₂= q ₂ is along n ₁ n ₂ . line of intersection of r . n ₃= q ₃ & r . n ₄= q ₄ is along n ₃ n ₄ . The two lines are perpendicular when ( n ₁ n ₂ ) ( n ₃ n ₄ )=0 ( n ₁ n ₃ ) ( n ₂ n ₄ )- ( n ₁ n ₄ ) ( n ₂ n ₃ )=0 (B) ( n ₁ n ₂ ) n ₄=0= ( n ₂ n ₃ ) n ₄= ( n ₁ n ₃ ) n ₄ (C) ( n ₁ n ₂ ) ( n ₃ n ₄ )=0 [ array lll n ₁ & n ₂ & n ₄ array ] n ₃= [ array lll n ₁ & n ₂ & n ₃ array ] n ₄ (D) Plane contains line along n ₁ n ₂ . Also plane is parallel to the line along n ₃ n ₄ . But do

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