What surface is represented by the equation z=3 ?

Expert Answers
justaguide eNotes educator| Certified Educator

The surface represented by z = 3 is a plane consisting of all point that have the z co-ordinate as 3.

The x and y co-ordinates can take on any value.

The only constraint we have here is that all points that form the plane have the z-coordinate as 3.

The surface represented by z = 3 consists of all points that have the value of the z-coordinate as 3.

giorgiana1976 | Student

In general, an equation x = k, represents a plane, parallel to y-z plane.

The equation y = k, represents a plane, parallel to x-z plane.

The equation z = k, represents a plane, parallel to x-y plane.

The equation z = 3 represents the set of all points  whose z coordinate is 3.

Therefore, the equation z = 3 is the horizontal plane, that is parallel to x-y plane and it is located 3 units above x-y plane.