Q. 125.0( 2 Votes )

Find the equation

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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