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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

If three planes P₁ 2 x+y+z-1=0, P₂=x-y+z-2=0 and P₃ x-y+3 z-5=0 intersects each other at point P on X O Y plane and at point Q on Y O Z plane, where O is the origin then identify the correct statement(s)?

Options

  1. AThe value of is 4 .
  2. BStraight line perpendicular to plane P₃ and passing through P is x-1 4 = y+1 -1 = z 3 .
  3. CThe length of projection of P Q on x -axis is 1 .
  4. DCentroid of the triangle O P Q is ( 1 3 , -1 2 , 1 2 )

Correct answer

D. Centroid of the triangle O P Q is ( 1 3 , -1 2 , 1 2 )

Step-by-step solution

Three planes meet at two points it means they have infinitely many solutions, so aligned & | array ccc 2 & 1 & 1 1 & -1 & 1 & -1 & 3 array |=0 & 2(-3+1)-1(3+1)+ (1+1)=0 . =4 & P₁: 2 x+y+z=1 & P₂: x-y+z=2 & P₃: 4 x-y+3 z=5 & P on X O Y plane =(1,-1,0) aligned (which can be obtained by putting z=0 in any two of the given planes.) Q on Y O Z plane (0, -1 2 , 3 2 ) (which can be obtained by putting x=0 in any two of the given planes.) Straight line perpendicular to plane P₃ passing through P is : gathered x-1 4 = y+1 -

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