# Closest point to the origin

Find the closest point of the surface:

xy + xz + yz = 1 to the origin.

and

x^2 + y^2 - Z^2 = 1 to the origin.

https://brainmass.com/math/linear-transformation/closest-point-origin-207311

#### Solution Preview

Find the closest point of the surface:

(1) xy + xz + yz = 1 to the origin.

Actually we want to find the minimum value of subject to the constraints.

We use Lagrange multiplier

(1) Let

(1)

(2)

...

#### Solution Summary

The solution provides an example of finding the closest point of given surfaces to the origin.

$2.19