Chapter 11.1, Problem 23E

To determine

Tofind:Theoctant in which the point $\left(xy<0\right)$ is located.

Answer to Problem 23E

Thepoint $\left(xy<0\right)$ is located in Octant II, IV, VI and VIII.

Explanation of Solution

Given information:

The given point is $\left(xy<0\right)$ .

Calculation:

An octant is defined as a division of three-dimensional coordinate system into eight divisions that are separated by the planes.

  

According to the question, the product of x and y is less than 0. So, this is possible when either $x$ is negative or y is negative.

In the question, the value of z is not given. So, we can consider the positive and the negative value of z .

When the value of $x$ and z is less than 0 and y is greater than 0, the values will lie in VI.

When the value of y and z is less than 0 and x is greater than 0, the values will lie in VIII.

When the value of y and z is greater than 0 and x is less than 0, the values will lie in II.

When the value of x and z is greater than 0 and y is less than 0, the values will lie in IV.

Therefore, the point $\left(xy<0\right)$ is located in Octant II, IV, VI and VIII.