Question

In Exercises \(7-18,\) determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(z=6\)

Short answer

The location of the point (x, y, z) that satisfies the condition z=6 is denoted as (x, y, 6), where x and y can be any real number.

Step-by-step solution

Understand the problem

We are tasked to find the location of a point in a three-dimensional space. In 3D geometry, any point can be represented by three coordinates (x, y, z). Here we are provided with the condition z=6. So our task is to find the coordinates (x, y, z) which fulfill this condition.

Realize the condition

The condition given is z=6. This means that, regardless of the values of the other two coordinates (x and y), z must equal 6. In a 3-dimensional space, this condition results in a flat plane parallel to the x-y plane at a distance of 6 units above it.

Formulate the solution

Given the condition z=6, any point that exists on the plane z=6 will satisfy this condition. Therefore, the coordinates of such points can be represented as (x, y, 6), where x and y can be any real number.