/*! 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} Q. 13 What point is symmetric to the p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 13 (page 788)

What point is symmetric to the point \((3, 鈭�7, 鈭�4)\) with respect to the plane \(z = 1\)?

Short Answer

Expert verified

The point that is symmetric to the point \((3, 鈭�7, 鈭�4)\) with respect to the plane\( z = 1\) is \((3,-7, 6)\)

Step by step solution

01

Step 1. Given information

The given point is \((3, 鈭�7, 鈭�4)\).

Here, both the y and z coordinates are negative and the x-coordinate is positive. Thus, the above point lies in the fourth octant.

02

Step 2. Finding the required symmetric point.

As the given point lies in the fourth octant, its symmetric point with respect to the plane \(z=1\) will lie at the right of this plane (third octant) where the z-coordinate is positive.

Here given plane is \(z=1\)

Distance between the z-coordinate of the given point i.e -4 and plane z=1 is given as:

\(z = 1-(-4)\)

= 5

Therefore, the new z-coordinate in the third octant is :
z = 1+5 =6

Therefore, The point that is symmetric to the point \((3, 鈭�7, 鈭�4)\) with respect to the plane \(z = 1\) is \((3,-7, 6)\).

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 mass of a 30-centimeter rod with square cross sections of side length 2 centimeters, given that the density of the rod x centimeters from the left end is 蟻(x) =10路5+0路01527x2 grams per cubic centimeter.

A function f that satisfies the hypotheses of Rolle鈥檚 Theorem on [鈭�2, 2] and for which there are exactly three values c 鈭� (鈭�2, 2) that satisfy the conclusion of the theorem .

Use the definition of the derivative to find f'for each function fin Exercises 39-54

f(x)=2x+1

Find a unit vector in the direction opposite to3,4,5.

Find the norm of the vector.v=12,13,14
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.