A) \[\frac{\sqrt{14}}{2}\]
B) \[\sqrt{7}\]
C) \[\frac{7}{2}\]
D) \[\frac{\sqrt{7}}{2}\]
Correct Answer: A
Solution :
Given equation of sphere is \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x-2y-3z=0\] \[\therefore \] Centre is \[\left( \frac{1}{2},1,\frac{3}{2} \right).\] \[\therefore \] Radius \[=\sqrt{{{\left( \frac{1}{2} \right)}^{2}}+{{(1)}^{2}}+{{\left( \frac{3}{2} \right)}^{2}}-0}\] \[=\sqrt{\frac{1}{4}+1+\frac{9}{4}}=\sqrt{\frac{14}{4}}\] \[=\frac{\sqrt{14}}{2}\]
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