/*! 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 17 Determine the location of a poin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 17

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(x y z<0\)

Short Answer

Expert verified
The location of a point \((x, y, z)\) that satisfies the condition \(x y z<0\) would be in the either of the following regions: (i) \(x>0, y>0, z<0\), (ii) \(x>0, y<0, z>0\), (iii) \(x<0, y>0, z>0\), and (iv) \(x<0, y<0, z<0\).

Step by step solution

01

Interpret the inequality

The inequality x*y*z<0 has a negative result. Thus, in the multiplication of x, y, and z, one or three of them must be negative. This is because the multiplication of an odd number of negative numbers results in a negative product.
02

Determine the possible regions

There are four different regions that can have a negative product: (i) when x>0, y>0, z<0, (ii) when x>0, y<0, z>0, (iii) when x<0, y>0, z>0, and (iv) when x<0, y<0, z<0. These areas are, respectively: the area behind the x-y plane, the area below the x-z plane, the area to the left of the y-z plane, and the area within the octant formed by all three planes.
03

Formulate the final answer

The location of a point (x, y, z) that fulfills the condition x*y*z < 0 would be in either of these four regions: (i) x>0, y>0, z<0, (ii) x>0, y<0, z>0, (iii) x<0, y>0, z>0, and (iv) x<0, y<0, z<0.

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.

Determine which of the vectors is (are) parallel to \(\mathrm{z}\). Use a graphing utility to confirm your results. \(\mathbf{z}\) has initial point (5,4,1) and terminal point (-2,-4,4) (a) \langle 7,6,2\rangle (b) \langle 14,16,-6\rangle

Find each scalar multiple of \(v\) and sketch its graph. \(\mathbf{v}=\langle 2,-2,1\rangle\) (a) - \(\mathbf{v}\) (b) \(2 \mathbf{v}\) (c) \(\frac{1}{2} \mathbf{v}\) (d) \(\frac{5}{2} \mathbf{v}\)

Let \(A, B,\) and \(C\) be vertices of a triangle. Find \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}\)

Find a unit vector \((a)\) in the direction of \(\mathbf{u}\) and \((\mathbf{b})\) in the direction opposite \(\mathbf{u}\) \(\mathbf{u}=\langle 8,0,0\rangle\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.