A) \[\left( \frac{a}{2},\frac{b}{2},\frac{c}{2} \right)\]
B) \[\left( -\frac{a}{2},-\frac{b}{2},\frac{c}{2} \right)\]
C) \[\left( \frac{a}{2},\,\,-\frac{b}{2},\,-\frac{c}{2} \right)\]
D) \[\left( -\frac{a}{2}\,\,,\frac{b}{2},\,-\frac{c}{2} \right)\]
Correct Answer: A
Solution :
Let point be \[(x,\,y,\,z),\] then \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] = \[{{(x-a)}^{2}}+{{y}^{2}}+{{z}^{2}}={{x}^{2}}+{{(y-b)}^{2}}+{{z}^{2}}={{x}^{2}}+{{y}^{2}}+{{(z-c)}^{2}}\] Therefore \[x=\frac{a}{2},\,\,y=\frac{b}{2}\] and \[z=\frac{c}{2}\].
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