Q. 115.0( 2 Votes )

Find the equation of the plane through the line of intersection of the planes and and which is perpendicular to the plane ?[CBSE 2013]

Answer :

We know that, the equation of a plane through the line of intersection of the planes


and


is given by


So, equation of the plane passing through the line of intersection of the plane


and is given by


[] + k[] = 0


.[ + k[] – 4 + 5k = 0 …… (1)


We know that two planes perpendicular if


.


Given that plane (1) is perpendicular to the plane



Using (1)and (3) in equation (2),


[ + k()]( = 0


(1 + 2k)(5) + (2 + k)(3) + (3 – k)( – 6) = 0


5 + 10k + 6 + 3k – 18 + 6k = 0


19k – 7 = 0


k =


Put the value of k in equation (1),


.[)] – 4 + 5() = 0


.[] –


.[] –


Multiplying by 19,



Equation of required plane is,



33x + 45y + 50z – 41 = 0

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