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

Question

The shortest distance from the point (1,2,-1) to the surface of the sphere x2+y2+z2=54 is (A)  3√6  (B)  2√6  (C)  √6  (D)  2

Tardigrade Admin · Accepted Answer

The equation of sphere is x2+y2+z2=54 The centre and radius of this sphere are (0, 0, 0) and √54, ie, 3√6 . Distance between (1, 2, -1) and (0, 0, 0) is √6 . ∴ Shortest distance between point (1,2,-1) and surface of the sphere =3√6-√6 =2√6

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

$36$

$26$

$6$

$2$

$4$

The equation of sphere is $x^{2} + y^{2} + z^{2} = 54$ The centre and radius of this sphere are (0, 0, 0) and $54,$ ie, $36$ . Distance between (1, 2, -1) and (0, 0, 0) is $6$ .
$∴$ Shortest distance between point $(1, 2, - 1)$ and surface of the sphere
$= 36 - 6$
$= 26$

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

36​

26​

6​

2

4

The equation of sphere is x2+y2+z2=54 The centre and radius of this sphere are (0, 0, 0) and 54​, ie, 36​ . Distance between (1, 2, -1) and (0, 0, 0) is 6​ . ∴ Shortest distance between point (1,2,−1) and surface of the sphere =36​−6​ =26​

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

$36$

$26$

$6$

$2$

$4$

The equation of sphere is $x^{2} + y^{2} + z^{2} = 54$ The centre and radius of this sphere are (0, 0, 0) and $54,$ ie, $36$ . Distance between (1, 2, -1) and (0, 0, 0) is $6$ .
$∴$ Shortest distance between point $(1, 2, - 1)$ and surface of the sphere
$= 36 - 6$
$= 26$