/*! 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 23. Find the equations of the planes... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 23. (page 845)

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

The plane contains the point (2,鈭�1,6)and is normal to the vector鉄�2,-1,6鉄�

Short Answer

Expert verified

The equation of the plane that is determined by the given conditions is

2x-y+6z-41=0.

Step by step solution

01

Given information

The plane that contains the point (2,-1,6)and is normal to the vector 鉄�2,-1,6鉄�

02

Calculation

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

The equation of the plane with r0a point that lies in the plane and na vector normal to the plane is given by:

n路r-r0=0

The normal vector is:

n=鉄�2,-1,6鉄�

The point r0is:

r0=(2,-1,6)

03

Calculation

The equation of the plane that contains the point (2,-1,6)and is normal to the vector 鉄�2,-1,6鉄�is:

鉄�2,-1,6鉄�路(鉄�x,y,z鉄�-(2,-1,6))=0(Substitution)

2x-y+6z-(2(2)-1(-1)+6(6))=0(Simplify)2x-y+6z-(4+1+36)=02x-y+6z-41=0

Thus, the equation of the plane that is determined by the given conditions is

2x-y+6z-41=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

If u脳v=uv, what is the geometric relationship between u and v?

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,鈭�2),Q(鈭�2,0),R(1,鈭�5)

(Hint: Think of the xy-plane as part of 鈩�3.)

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(1,6),Q(0,鈭�3),R(鈭�5,4)

(Hint: Think of the xy-plane as part of 鈩�3.)

In Exercises 24-27, find compuv, projuv, and the component of v orthogonal tou.

u=1,2,v=3,5

Find the norm of the vector.v=3,鈭�4
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.