Question

To describe: The representation of inequality \(x \ge - 3\) in \({\mathbb{R}^3}\).

Short answer

It represent the plane is \(yz\)plane in \({\mathbb{R}^3}\).

Step-by-step solution

Concept of \({\mathbb{R}^3}\)

\({\mathbb{R}^3}\)is the three dimensional coordinate system which contains\(x\),\(y\), and\(z\)-coordinates.

Interpret the representation of given equation in \({\mathbb{R}^3}\)

The given inequality in \({\mathbb{R}^3}\) is \(x \ge - 3\).

It is known that in three dimensional coordinate system containing \(x\), \(y\), and \(z\)-coordinates; points on this coordinate is represented by \((x,y,z)\).

The inequality \(x \ge - 3\) in \({\mathbb{R}^3}\) represents the set \(\{ (x,y,z)\mid x \ge - 3\} \).

It is the set of all points in \({\mathbb{R}^3}\) whose \(x\)-coordinate is greater than or equal to \( - 3\) and \(y\), \(z\)-coordinates are any values.

Hence, it represent the plane is \(yz\)plane in \({\mathbb{R}^3}\).