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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph: Let a₁ x+b₁ y+c₁ z+d₁=0 and a₂ x+b₂ y+c₂ z+d₂=0 be two planes, where d₁, d₂ 0 . Then origin lies in acute angle if a₁ a₂+b₁ b₂+c₁ c₂ 0 and origin lies in obtuse angle if a₁ a₂+b₁ b₂+c₁ c₂ 0 . Further point (x₁, y₁, z₁ ) and origin both lie either in acute angle or in obtuse angle, if (a₁ x₁+b₁ y₁+c₁ z₁+d₁ ) (a₂ x₁+b₂ y₁+c₂ z₁+d₂ ) 0 . One of (x₁, y₁, z₁ ) and origin lie in acute angle and the other in obtu

Options

  1. AO and P both lie in acute angle between the planes
  2. BO and P both lie in obtuse angle
  3. CO lies in acute angle, P lies in obtuse angle
  4. DO lies in obtuse angle, P lies an acute angle

Correct answer

C. O lies in acute angle, P lies in obtuse angle

Step-by-step solution

1 2+2 1-3 3 0 Origin lies in acute angle Also (2+2(-1)-3(2)+5)(2 2-1+3 2+1)=(-1)(10) 0 P lies in obtuse angle

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