Question

What does the equation y = 2 represent in R³?

Answer 1

The equation y = 2 in R³ represents a plane parallel to the xz-plane, two units above it along the y-axis, comprising points with any x and z coordinates but with a constant y coordinate of 2.

Step-by-step explanation:

The equation y = 2 represents a plane in 3-dimensional space, specifically in R³ (three-dimensional real number space). This plane is parallel to the xz-plane and is located two units above the xz-plane along the y-axis. In this equation, 'y' is the y-coordinate of any point on the plane, and it is constantly equal to 2, regardless of the values of 'x' and 'z' coordinates. Hence, every point on this plane has the form (x, 2, z), where 'x' and 'z' can be any real numbers.

Answer 2

In R³, the equation y = 2 represents a horizontal plane that is parallel to the x-z plane and passes through the y-axis at y = 2.

Step-by-step explanation:

In the context of R³, the equation y = 2 represents a horizontal plane that is parallel to the x-z plane and passes through the y-axis at y = 2. This means that all points on this plane have a y-coordinate of 2, while the x and z coordinates can vary.