A) \[\left( -1,-1,-1 \right)\]
B) \[(1,1,1)\]
C) \[\left( -1,-1,\,\,1 \right)\]
D) \[\left( 1,-1,\,\,1 \right)\]
Correct Answer: D
Solution :
Let \[A\,\,(1,\,2,\,3),\,\,\,B\left( \frac{-7}{3},\frac{-4}{3},\frac{-1}{3} \right)\] Mid-point of \[AB\equiv \left( \frac{-2}{3},\frac{1}{3},\frac{4}{3} \right)\] Let equation of plane is \[a\left( x+\frac{2}{3} \right)+b\left( y-\frac{1}{3} \right)+c\left( z-\frac{4}{3} \right)=0\] ... (i) dr's of \[AB=\frac{10}{3},\frac{10}{3},\frac{10}{3}\] \[\therefore \] Equation of plane is \[x+\frac{2}{3}+y-\frac{1}{3}+z-\frac{4}{3}=0\] \[\Rightarrow \,\,\,\,\,x+y+z=1\] \[\therefore \] (1, -1, +1) lies on the plane
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