/*! 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 21. Find the equations of the planes... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 21. (page 845)

Find the equations of the planes determined by the given conditions.

The plane contains the origin and is normal to the vector4,鈭�1,5

Short Answer

Expert verified

The equation of the plane that is determined by the given conditions is 4x-1y+5z=0

Step by step solution

01

Given information

The plane that is normal to the vector4,鈭�1,5 and contains the origin.

02

Calculation

Consider the plane that is normal to the vector鉄�4,-1,5鉄� and contains the origin.

The goal is to determine the plane equation that is determined by the given conditions.

The equation of the plane with r0 a point that lies in the plane and n a vector normal to the plane is given by:

n路r-r0=0

The normal vector is:

n=鉄�4,-1,5鉄�

The point r0is:

r0=(0,0,0)

03

Calculation

The plane that contains the origin and is normal to the vector 鉄�4,-1,5鉄� has the equation:

鉄�4,-1,5鉄�路(鉄�x,y,z鉄�-鉄�0,0,0鉄�)=0(Substitution)鉄�4,-1,5鉄�路鉄�x,y,z鉄�=0(Simplify)4x-1y+5z=0

Thus, the equation of the plane that is determined by the given conditions is 4x-1y+5z=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

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=1,2,v=3,5

1鈭� that approaches (a)1,(b)e,(c)鈭�.

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=13,-23

Sketch the parallelogram determined by the two vectors (1,2)and (3,鈭�1). How can you use the cross product to find the area of this parallelogram?

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v脳wandw脳v
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.