A) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=3\]
B) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6\]
C) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=9\]
D) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12\]
Correct Answer: C
Solution :
[c] Let the variable point be \[(\alpha ,\beta ,\gamma )\]then according to question \[{{\left( \frac{\left| \alpha +\beta +\gamma \right|}{\sqrt{3}} \right)}^{2}}+{{\left( \frac{\left| \alpha -\gamma \right|}{\sqrt{2}} \right)}^{2}}+{{\left( \frac{\left| \alpha -2\beta +\gamma \right|}{\sqrt{6}} \right)}^{2}}=9\] \[\Rightarrow {{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}=9.\] So, the locus of the point is \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=9\]
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