Equation of the pane passing through the points `(2,2,1)a n d(9,3,6),a n d_|_` to the plane `2x+6y+6z-1=0` is a. `3x+4y+5z=9` b. `3x+4y-5z=9` c. `3x+4y-5z=9` d. none of these

Options

A. `3x+4y+5z=9`
B. `3x+4y-5z=9`
C. `3x+4y-5z=9`
D. none of these

Answer

b

Explanation

Any plane through `(2, 2, 1)` is
`" "a(x-2)+b(y-2)+c(z-1)=0`
It passes through `(9, 3, 6)` if `7a+b+5c=0" "` (ii)
Also (i) is perpendicular to `2x+6y+6z-1=0`, we have
`" "2a+6b+6c=0`
`therefore" "a+3b+ 3c=0" "`(iii)
`therefore " "(a)/(-12)= (b)/(-16)= (c)/(20) or (a)/(3)= (b)/(4)= (c)/(-5)" "` [from (ii) and (iii)]
Therefore, the required plane is `3(x-2)+ 4(y-2)-5(z-1)=0 or 3x+4y-5z-9=0`