/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Determine the location of a poin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 15

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(x y>0, \quad z=-3\)

Short Answer

Expert verified
The point \((x, y, z)\) satisfying the given conditions is located either in the first quadrant (where \(x\) and \(y\) are both positive) or in the third quadrant (where \(x\) and \(y\) are both negative), with the \(z\)-coordinate being -3 in both cases.

Step by step solution

01

Understand Conditions

The conditions given in the problem are \(x y>0\) and \(z=-3\). The first condition implies that the product of \(x\) and \(y\) should be positive, which is only possible when \(x\) and \(y\) have the same sign; i.e., they are either both positive or both negative. The second condition directly states that \(z\) is -3.
02

Apply First Condition

When \(x y>0\), this means that \(x\) and \(y\) are either both positive or both negative. So, the point \((x, y, z)\) is in either the first quadrant (where \(x\) and \(y\) are both positive) or the third quadrant (where \(x\) and \(y\) are both negative) in the xy-plane.
03

Apply Second Condition

The \(z=-3\) condition is straightforward. Regardless of the position of the point \((x, y)\) in the xy-plane, its \(z\)-coordinate is always -3.
04

Combine Conditions

Combining the results from step 2 and step 3, the point \((x, y, z)\) satisfying the given conditions is found either in the positive x and y region with \(z=-3\) (first quadrant), or in the negative x and y region with \(z=-3\) (third quadrant).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the angle between the diagonal of a cube and the diagonal of one of its sides.

Sketch the vector \(v\) and write its component form. \(\mathbf{v}\) lies in the \(x z\) -plane, has magnitude \(5,\) and makes an angle of \(45^{\circ}\) with the positive \(z\) -axis.

(a) find the projection of \(\mathbf{u}\) onto \(\mathbf{v}\), and (b) find the vector component of u orthogonal to v. $$ \mathbf{u}=\langle 2,-3\rangle, \quad \mathbf{v}=\langle 3,2\rangle $$

The vector \(v\) and its initial point are given. Find the terminal point. \(\mathbf{v}=\left\langle 1,-\frac{2}{3}, \frac{1}{2}\right\rangle\) Initial point: \(\left(0,2, \frac{5}{2}\right)\)

In Exercises 61 and \(62,\) sketch the solid that has the given description in cylindrical coordinates. $$ 0 \leq \theta \leq 2 \pi, 2 \leq r \leq 4, z^{2} \leq-r^{2}+6 r-8 $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.