CGPET 2018 Solved Paper

Equations of the given planesx+y+z−6=0 .......(i)
and 2x+3y+4z+5=0 .......(ii)
The equation of the plane passing through the line of intersection of the plane Eqs. (i) and (ii).
x+y+z−6+λ(2x+3y +4z+5)=0 ........ (iii)
∵ Plane passing through the point (1,1,1).
Hence, 1+1+1−6+λ[2(1)+3(1) +4(1)+5]=0
⇒−3+14λ=0[ from Eq. (iii) ]
⇒λ=

3

14

Put the value of λ in Eq. (iii).
x+y+z−6+

3

14

(2x+3y +4z+5)=0
⇒14x+14y+14z−84+6x+9y +12z+15=0
⇒20x+23y+26z=69