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The shortest distance from the origin to...

The shortest distance from the origin to a variable point on the sphere `(x-2)^(2)+(y-3)^(2)+(z-6)^(2)=1` is-

A

5

B

6

C

7

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Sphere `x^(2)+y^(2)+z^(2)-4x-6x-12z+48=0`
Centre (2,3,6)
radius `=sqrt(4+9+36-48)=1`
distance between centre and origin `=sqrt(4+9+36)=7`
shortest distance =7-1-6 (Origin lies outside the sphere)
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