the equation of a plane through the line of intersection the planes `x+2y=3,y-2z+1=0` and perpendicular to the first plane is:

Options

A. `2x-y-10z=9`
B. `2x-y+7z=11`
C. `2x-y+10z=11`
D. `2x-y-9z=10`

Answer

C

Explanation

Intersection of two planes is
`(X+2y-3)+lamda(y-2z+1)=0`
`rArr" "x+(2+lamda)y-2lamdaz+lamda-3=0` . . . (i)
`because` Plane (i) is perpendicular to plane `x+2y-3=0`
`:." "1(1)+2(2+lamda)+0(-2lamda)=0rArrlamda=-(5)/(2)`
On putting the value of `lamda` in Eq (i), we get
`x+(2-(5)/(2))y-2((-5)/(2))z-(5)/(2)-3=0`
`rArr" "2x-y+10z=11`