A) \[3\sqrt{6}\]
B) \[2\sqrt{6}\]
C) \[\sqrt{6}\]
D) \[2\]
E) \[4\]
Correct Answer: B
Solution :
The equation of sphere is \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=54\] The centre and radius of this sphere are (0, 0, 0) and\[\sqrt{54},\]ie,\[3\sqrt{6}\]. Distance between (1, 2, -1) and (0, 0, 0) is\[\sqrt{6}\]. \[\therefore \]Shortest distance between point \[(1,2,-1)\] and surface of the sphere \[=3\sqrt{6}-\sqrt{6}\] \[=2\sqrt{6}\]
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