The equation of the plane passing through the points (0,1,2) and (-1,0,3) and perpendicular to the plane `2x+3y+z=5` is

Options

A. `3x-4y+18z+32=0`
B. `3x+4y-18z+32=0`
C. `4x+3y-17z+31=0`
D. `4x-3y+z+1=0`

Answer

D

Explanation

Any plane passing through (0,1,2) is
`a(x-0)+b(y-1)+c(z-2)=0`
`impliesax+b(y-1)+c(z-2)=0`…………….i
Since it is passing through
`(-1,0,3)` we get
`-a-b+c=0` ………..ii
Also Eq. i is perpendicular to
`2x+3y+z=5`
`:.2a+3b+c=0`...........iii
On solving eqs ii and iii we get
`a/(-4)=b./3=c/(-1)`
`:.` From eq. i
`-4x+3(y-1)-1(z-2)=0`
`implies4x-3y+z+1=0`