Question

The shortest distance from the point $ (1,2,-1) $ to the surface of the sphere $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}=54 $ is

• A. $ 3\sqrt{6} $
• B. $ 2\sqrt{6} $
• C. $ \sqrt{6} $
• D. $ 2 $
• E. $ 4 $

Answer 1

Answer: (B)

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} $