Question

Sketch the planes. $$ z=-2 $$

Name: Problem 35, Chapter 15: Finite Mathematics and Applied Calculus
Uploaded: 2021-10-16T03:07:18-08:00
Duration: 1 min 58 s
Channel: Harshita Goel
Description: Sketch the planes. z=-2

   Sketch the planes.
$$
z=-2
$$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 15, Problem 35

Instant Answer

Solved by Expert Harshita Goel

10/16/2021

Step 1

The equation $z=-2$ represents a plane in three-dimensional space. This plane is parallel to the xy-plane and is located 2 units below the origin along the z-axis. Show more…

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Sketch the planes. $$ z=-2 $$

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Key Concepts

Cartesian Coordinate System

The Cartesian coordinate system is a framework that allows us to specify points in space using perpendicular axes, typically labeled x, y, and z. It provides the foundation for plotting equations of geometric objects like lines, curves, and planes in three dimensions.

Plane Equation

A plane in three-dimensional space can be defined by an equation, often written in the form ax + by + cz + d = 0. This equation represents all the points that satisfy the condition, and different forms emphasize various orientations of the plane. In the context of the equation given, the plane equation simplifies to a specific type.

Horizontal Plane

A horizontal plane is one that runs parallel to the x-y plane and is characterized by a constant z-value across all points. The equation z = -2 indicates that every point on this plane has a z-coordinate of -2, meaning the plane is flat and parallel to the x-y plane, positioned below it by 2 units.

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