A) 3
B) 0
C) \[1/\sqrt{6}\]
D) \[2/\sqrt{6}\]
Correct Answer: D
Solution :
Let the equation of plane passing through the point P (-1, -1,1) is \[a(x+1)+b(y+1)+c(z-1)=0\] ?.(i) which passes through the points Q (0,1,1) and R (0,0,2). \[\therefore \] \[a+2b+0c=0\] and \[a+b+c=0\] \[\Rightarrow \] \[\frac{a}{2-0}=-\frac{b}{1-0}=\frac{c}{1-2}\] \[\Rightarrow \] \[\frac{a}{2}=\frac{b}{-1}=\frac{c}{-1}\] From Eq. (i), \[2(x+1)-y(y+1)-1(z-1)=0\] \[\Rightarrow \] \[2x-y-z+2=0\] \[\therefore \]Distance of plane from point (0, 0, 0) \[=\frac{0+0+0+2}{\sqrt{{{2}^{2}}+{{(-1)}^{2}}+{{(-1)}^{2}}}}=\frac{2}{\sqrt{6}}\]You need to login to perform this action.
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