question_answer

The shortest distance from the point\[(1,2,-1)\] to the surface of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=24\] is:

A)  \[3\sqrt{6}\] unit            

B)  \[\sqrt{6}\] unit

C)  \[2\sqrt{6}\]unit       

D)         2 unit

E)  \[3\sqrt{2}\]unit

Correct Answer: B

Solution :

The given point\[(1,2,-1)\]lies inside the sphere. \[\because \]Centre of sphere is (0, 0, 0), then the shortest distance between\[(1,2,-1)\]and surface of sphere \[=\sqrt{OQ}-\sqrt{OP}\] \[=\sqrt{24}-\sqrt{6}=2\sqrt{6}-\sqrt{6}\] \[=\sqrt{6}\,unit\]