JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry QA 10/ JEE question on equation of plane passing through the line of intersection of two planes and at a given distance from a given point

1. Physics Helpline
L K Satapathy
3D Geometry QA 10

2. Physics Helpline
L K Satapathy
3 D Geometry QA 10
Question : The equation of a plane passing through the line of intersection of the
planes x + 2y + 3z = 2 and x – y + z = 3 and at a distance of units from the
point ( 3 , 1 , – 1 ) is
( )5 11 17 ( ) 2 3 2 1 ( ) 3 ( ) 2 1 2a x y z b x y c x y z d x y           
Answer :
Equation of plane passing through the line of intersection of the planes
x + 2y + 3z = 2 and x – y + z = 3 is given by
( 2 3 2) ( 3) 0x y z x y z       
(1 ) (2 ) (3 ) 2 3 0 . . . (1)x y z           
Plane (1) is at a distance of units from the point ( 3 , 1 , – 1 )
2
3
2 2 2
3(1 ) (2 ) (3 ) 2 3 2
3(1 ) (2 ) (3 )
   
  
      
 
    
2
3

3. Physics Helpline
L K Satapathy
3 D Geometry QA 10
2 2 2
3 3 2 3 2 3 2
32 1 4 4 6 9
   
     
       
       
2 2
2 2 1
3 33 4 14 3 4 14
 
   
   
   
2 2 73 3 4 14 4 14 0
2
             
7(1) ( 2 3 2) ( 3) 0
2
x y z x y z        
2( 2 3 2) 7( 3) 0x y z x y z        
5 11 17 0x y z     
5 1 [ ]1 17x y z Ans   
Correct option = (a)

4. Physics Helpline
L K Satapathy
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