CGPET 2016 Solved Paper

Given planes P1:x+2y+3z−4=0
P2:2x+y−z+5=0
The equation pf plane through intersection of P1 and P2 is
P1λP2=0
⇒ (x+2y+3z−4)+λ(2x+y−z+5)=0
⇒ x(1+2λ)+y(2+λ)+z(3−λ)+(5λ−4)=0 ....(i)
Since, the plane is perpendicular to
5x+3y+6z+8=0
∴ a1a2+b1b2+c1c2=0
⇒ (1+2λ)(5)+(2+λ)(3)+(3−λ)(6)=0
⇒ 5+10λ+6+3λ+18−6λ=0
⇒ 7λ+29=0
∴ λ=

−29

7

Now, equation of the plane is
(x+2y+3z−4)+(

−29

7

)(2x+y−z+5)=0
⇒7x+14y+21z−28−58x−29y+29z−145=0
⇒ −51x−15y+50z−173=0
⇒ 51x+15y−50z=−173