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Chapter 11: Problem 3

Describe the plane \(x=4\)

Short Answer

Expert verified
Question: Describe and graph the plane represented by the equation x = 4. Answer: The plane x = 4 is a vertical plane parallel to the yz-plane passing through all points with an x-coordinate of 4. To graph this plane, draw a 3D coordinate system and locate the point (4, 0, 0) on the x-axis. Then, draw a vertical plane parallel to the yz-plane passing through (4, 0, 0) and all points with an x-coordinate of 4.

Step by step solution

01

Identify the given equation

The given equation is x = 4, which represents a plane in 3D space.
02

Describe the plane

Since the equation is x = 4, it means that the plane consists of all points in the 3D space with x-coordinate equal to 4. The plane is parallel to the yz-plane and passes through all points with x-coordinate equal to 4.
03

Graph the plane

To graph the plane, first, draw a 3D coordinate system with x, y, and z axes. Then, locate the point (4, 0, 0) on the x-axis as this is the point where the plane intersects the x-axis, since its x-coordinate is 4. Now, draw a vertical plane parallel to the yz-plane that passes through (4, 0, 0) and all points with x-coordinate equal to 4. This is the graphical representation of the plane x = 4.

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Most popular questions from this chapter

Compute \(\mathbf{r}^{\prime \prime}(t)\) and \(\mathbf{r}^{\prime \prime \prime}(t)\) for the following functions. $$\mathbf{r}(t)=\tan t \mathbf{i}+\left(t+\frac{1}{t}\right) \mathbf{j}-\ln (t+1) \mathbf{k}$$

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