How do you find the point on the plane given by the equation 2x + y + 2z = 20 that is closest to the origin (0, 0, 0)?

To find the point on the plane represented by the equation 2x + y + 2z = 20 that is closest to the origin, we can employ the method of Lagrange multipliers or distance optimization techniques. Let’s go through the steps:

1. **Understanding the problem:** We need to minimize the distance from the origin to a point \