Find the equation of the plane through the points (2,2,1) and (9,3,6)` and perpendicular to the plane `2x+6y+6z=1`

Options

A. `x+2y-3z+5=0`
B. `2x-5y+4z-8=0`
C. `4x+5y-6z+3=0`
D. `3x+4y-5z-9=0`

Answer

d

Explanation

The equation of a plane passing through the point A(2,2,1) is
`a(x-2)+b(y-2)+c(z-1)0`…………………(i)
Since it passes through the point B(9,3,6), we have
`a(9-2)+b(3-2)+c(6-1)=0 rArr 7a+b+5c=0`………(ii)
Also, it being perpendicular to the plane `2x+6y+6z=1`, we have

`2a+6b+6c=0 rArr a+3b+3c=0`. ...............(iii)
On solving (ii) and (iii) by cross multiplication, we have
`a/(3-15)=b/(5-21)=c/(21-1) rArr a/-12=b/-16=c/20 rArr a/3=b/4=c/-5=k`
`rArr a=3k,b=4k` and `c=-5k`.
substituting these values in (i), we get
`3k(x-2)+4k(y-2)-5k(z-1)=0`
`rArr 3(x-2)+4(y-2)-5(z-1)=0 rArr 3x+4y-5z-9=0`.