Question

Sketch the planes. $$ z=4 $$

Name: Problem 36, Chapter 15: Finite Mathematics and Applied Calculus
Uploaded: 2021-10-16T03:07:40-08:00
Duration: 1 min 51 s
Channel: Harshita Goel
Description: Sketch the planes. z=4

   Sketch the planes.
$$
z=4
$$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 15, Problem 36

Instant Answer

Solved by Expert Harshita Goel

10/16/2021

Step 1

The equation is $z=4$. This equation represents a plane in three-dimensional space where the z-coordinate of every point on the plane is 4. Show more…

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Sketch the planes. $$ z=4 $$

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Key Concepts

Cartesian Coordinate System

A 3D coordinate system uses three perpendicular axes (x, y, and z) to represent points in space. It is fundamental for understanding and graphing objects like lines, surfaces, and planes in three dimensions.

Equation of a Plane

An equation of the form z = constant defines a plane in three-dimensional space. In this context, the equation specifies that no matter what values x and y take, the z-coordinate is always fixed, describing a flat, two-dimensional surface in a 3D environment.

Horizontal Planes

A horizontal plane is one that is parallel to the xy-plane. The equation z = 4 describes such a plane because all points on the plane have a z-coordinate of 4, meaning the plane is uniformly positioned above the xy-plane by 4 units.

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