Question

Sketch graphs of the equations in 3 -space. $$x=-3$$

   Sketch graphs of the equations in 3 -space.
$$x=-3$$

Calculus Multivariable

Calculus Multivariable

Deborah… 7th Edition

Chapter 12, Problem 13

Instant Answer

Solved by Expert Kayla Robinson

07/02/2021

Step 1

This equation implies that the x-coordinate of all points on the graph is fixed at -3. This means that the graph will be a plane parallel to the yz-plane, but shifted three units to the left along the x-axis. Show more…

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Sketch graphs of the equations in 3 -space. $$x=-3$$

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Key Concepts

Three-Dimensional Cartesian Coordinate System

This is the framework used to locate points in space using three values (x, y, z), each corresponding to distances along three mutually perpendicular axes. It allows the representation and analysis of geometric objects in a spatial context, crucial for understanding the structure of graphs in 3-space.

Planes in Three-Dimensional Space

A plane in 3-space is a flat, two-dimensional surface that extends infinitely within the space. Equations of the form x = constant define vertical planes that are parallel to the y-z plane, since the x-coordinate remains fixed while y and z can take any value.

Graphing Equations in 3-Space

Graphing in three dimensions involves plotting surfaces and curves using the three axes that represent the variables. When an equation such as x = -3 is graphed, it results in a plane where all points satisfy the condition by having a fixed x-coordinate, thus helping visualize spatial relationships and intersections in the Cartesian coordinate system.

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