A) \[3x+4y+5z=9\]
B) \[3x+4y-5z+9=0\]
C) \[3x+4y-5z-9=0\]
D) None of these
Correct Answer: C
Solution :
Equation of a plane passing through \[(2,\,\,2,\,\,1)\] is \[a(x-2)+b(y-2)+c(z-1)=0\] ... (i) This passes through \[(9,\,\,3,\,\,6)\] and is perpendicular to \[2x+6y+6z-1=0\] \[\therefore \] \[7a+b+5c=0\] and \[2a+6b+6c=0\] On solving above equations by cross-multiplication, we get \[\Rightarrow \] \[\frac{a}{6-30}=\frac{-b}{42-10}=\frac{c}{42-2}\] \[\Rightarrow \] \[\frac{a}{-24}=\frac{b}{-32}=\frac{c}{40}\] \[\Rightarrow \] \[\frac{a}{-3}=\frac{b}{-4}=\frac{c}{5}\] On substituting the values of \[a,\,\,b\] and \[c\] in Eq. (i), we get \[-3(x-2)-4(y-2)+5(z-1)=0\] or \[3x+4y-5z-9=0\] as the required plane.
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