Chapter 12.1, Problem 6E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

What does the equation *y* = 3 represent in ℝ^{3}? What does *z* = 5 represent? What does the pair of equations *y* = 3, *z* = 5 represent? In other words, describe the set of points (*x*, *y*, *z*) such that *y* = 3 and *z* = 5. Illustrate with a sketch.

To determine

**To explain:** The representation of equation

Explanation

*x*, *y*, and *z*-coordinates.

The equation
*y*-coordinate is 3 and *x*, *z*-coordinates are any values.

Therefore, the equation
*xz*-plane and is located 4 units to the right on the *xz*-plane.

The equation
*z*-coordinate is 5 and *x*, *y*-coordinates are any values.

Therefore, the equation
*xy*-plane and is located 5 units above the *xy*-plane

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