Question

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(x y z>0\)

Short answer

The point \((x, y, z)\) as per the inequality \(x y z > 0\), can be located either in the first octant where all coordinates are positive, or in the fourth, fifth, and seventh octants where one coordinate is positive and the other two are negative.

Step-by-step solution

Treat \(x y z>0\)

The inequality \(x y z>0\) implies that the product of the coordinates of a point \(x\), \(y\), and \(z\) must be positive.

Check conditions for variables

For a product of three numbers to be positive, either all three are positive, or one is positive and the other two are negative.

Determine the location

The point (x, y, z) will be located in the octants of three-dimensional space where all three coordinates are positive (the first octant), or where one coordinate is positive and the other two are negative (the fourth, fifth and seventh octants).