Question

Lagrange's Method of undetermined multipliers to
find shortest distance from the point (1, 2, 2) to the
sphere
x2 + y2 +z2 = 16​

Answer 1

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Answer 2

Concept :

A sphere is a spherical three-dimensional object with a circular form. The sphere has three axes: the x-axis, the y-axis, and the z-axis.

Given :

The point (1,2,2) and the equation of sphere is x²+y²+z² = 16.

Find :

To calculate shortest distance between (1,2,2) and the sphere.

Solution :

The shortest distance between any point to sphere is                                    = radius - (distance between centre and the point)

So, radius of the given circle is 4 as the centre of circle is (0,0,0) and radius is square root of 16.

The distance between centre and point is,

                          4 - √(2²+2²+1²)

                        = 4 - 3

                        = 1

Hence, the shortest distance between (1,2,2) and the given sphere is 1.