Question

The shortest distance from the point (1, 2, -1) to the surface of the sphere x² + y² + z² = 54 is

• (A) $3\sqrt{6}$
• (B) $2\sqrt{6}$
• (C) $\sqrt{6}$
• (D) 2

Answer 1

The Correct Option is B

Explanation:
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}$$$=2\sqrt{6}$$