Answer:
Option A
Explanation:
Equation of plane passing through (2,2,1) is
a(x-2) +b(y-2)+c(z-1)=0 .....(i)
Since , above plane is perpendicular to
3x+2y+4z+1=0
and 2x+y+3z+2=0
∴ 3a+2b+4c=0 ......(ii)
and 2a+b+3c=0 .....(iii)
[ \because for perpendicular , a1a2+b1b2+c1c2=0]
On multiplying eq.(iii) by 2 , we get
4a+2b+6c=0 ......(iv)
On subtracting eq.(iv) from eq.(ii) , we get
\Rightarrow c=\frac{-a}{2}
On putting c=\frac{-a}{2} in eq. (iii) , we get b = \frac{-a}{2}
on putting b = \frac{-a}{2} and c=\frac{-a}{2} in eq.(i)
we get a(x-2)-\frac{a}{2}(y-2)-\frac{a}{2}(z-1)=0
\Rightarrow\frac{a}{2}[2(x-2)-(y-2)-(z-1)]=0
\Rightarrow2x-4+y+2-z+1=0
\Rightarrow2x-y-z-1=0