Question

Sketch the surface in 3 -space. $$2 x+z=3$$

   Sketch the surface in 3 -space.
$$2 x+z=3$$

Calculus A New Horizon

Calculus A New Horizon

Howard Anton 6th Edition

Chapter 13, Problem 29

Instant Answer

Solved by Expert Linh Vu

09/03/2020

Step 1

The given equation is \(2x + z = 3\). This is a linear equation in three variables (x, y, z), which represents a plane in 3-space. Show more…

Show all steps

lock

Thanks for your feedback!

Sketch the surface in 3 -space. $$2 x+z=3$$

Play audio

Feedback

Powered by NumerAI

Linh Vu and 98 other subject Calculus 3 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Intercept Analysis

Determining the intercepts by setting two of the three coordinates to zero is an effective method for sketching a plane. This approach helps to identify key points where the plane crosses the coordinate axes, which in turn aids in accurately depicting the plane's location and orientation in the coordinate system.

Graphical Representation in 3-Space

Sketching in three-dimensional space involves plotting key points like intercepts and using the normal vector to understand the plane's tilt. Visualizing these elements helps in comprehending how the plane is oriented relative to the three axes, facilitating an accurate sketch of the surface.

Plane in Three-Dimensional Space

A plane in three-dimensional space is a flat, two-dimensional surface that extends infinitely in all directions within that space. It is typically described by a linear equation in three variables, and every point on the plane satisfies this equation.

Normal Vector

The coefficients of the variables in the plane's equation form the components of the normal vector, which is perpendicular to the plane. This vector is crucial for understanding the orientation of the plane in space.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later