A) \[(0,\,-1,0)\]
B) \[(0,\,1,-6)\]
C) \[\left( -\frac{3}{2},0,0 \right)\]
D) \[\left( -\frac{1}{2},0,0 \right)\]
Correct Answer: C
Solution :
Let the point on x-axis is \[(x,0,0)\] According to the question, \[\sqrt{{{(x-4)}^{2}}+{{(0-3)}^{2}}+{{(0-1)}^{2}}}\] \[=\sqrt{{{(x+2)}^{2}}+{{(0+6)}^{2}}+{{(0+2)}^{2}}}\] \[\Rightarrow \] \[{{x}^{2}}+16-8x+9+1={{x}^{2}}+4+4x+36+4\] \[\Rightarrow \] \[12x=26-44=-18\] \[\Rightarrow \] \[x=\frac{-18}{12}=\frac{-3}{2}\] Hence, required point is \[\left( \frac{-3}{2},0,0 \right)\].
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