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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 intersect each other at point P on XOY plane and at point Q on YOZ 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 OPQ is ( 1 3 ,- 1 2 , 1 2 )

Correct answer

D. centroid of the triangle OPQ is ( 1 3 ,- 1 2 , 1 2 )

Step-by-step solution

Three planes meet at two points it means they have infinite many solution, so aligned & | array ccc 2 & 1 & 1 1 & -1 & 1 & -1 & 3 array |=0 on solving =4 & P ₁: 2 x+y+z=1 & P ₂: x-y+z=2 & P ₃: 4 x-y+3 z=5 & P _ on XOY plane (1,-1,0) (Which can be obtained by putting z=0 in any two equations) & Q on Y O Z plane (0,- 1 2 , 3 2 ) (By putting x=0 in any two equations) aligned

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