A) \[(1,0,1)\]
B) (0, 1, 1)
C) \[(1,1,-1)\]
D) (1, 1, 0)
E) (1, 1, 1)
Correct Answer: E
Solution :
Let the point be \[(x,y,z)\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{(x-2)}^{2}}\,+{{y}^{2}}+{{z}^{2}},\] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{x}^{2}}+{{(y-2)}^{2}}+{{z}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{(x-2)}^{2}}\] \[+{{(y-2)}^{2}}+{{(z-2)}^{2}}\] Point (1, 1, 1) satisfies all the above equations.
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