/*! 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 .5. 聽Let P and Q be distinct points... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q .5. (page 833)

Let P and Q be distinct points in鈩�3 Provide a stepby-step procedure for finding the equation of the line containing P and Q

Short Answer

Expert verified

r(t)=(a,b,c)+t(伪-a,尾-b,纬-c)

And

The line equation as a vector function isr(t)=(a+(伪-a)t,b+(尾-b),c+(纬-c)t).

Step by step solution

01

Step 1:Given information

LetP(a,b,c)andQ(伪,尾,纬)are any two points.

02

Step 2:Explaination

To construct the equation find the direction vector along the line PQ鈫�of the given points.

The direction vector (d=伪-a,尾-b,纬-c)

To construct the equation choose the point Por Qand construct the equation.

Here take the pointP(a,b,c)and the direction vector d=(伪-a,尾-b,纬-c)

The formula to find the line Lequation as a vector function is as follows,

r(t)=P0+tdWhere, P0is the point and dis the direction vector.

For the pointP(a,b,c)and the direction vector $\d=(伪-a,尾-b,纬-c)the line equation is as follows,

r(t)=(a,b,c)+t(伪-a,尾-b,纬-c)

The line equation as a vector function isr(t)=(a+(伪-a)t,b+(尾-b),c+(纬-c)t).

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

How is the determinant of a 3 脳 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3)?

Find PQ鈫�

P=1,-2,5,Q=1,-7,-2

1鈭� that approaches (a)1,(b)e,(c)鈭�.

Find u+vand u-v. Also, sketch u,v,u+vand u-v.

role="math" localid="1649572653771" u=2,-6,v=6,2,

What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v and w? How do you find the volume of the parallelepiped determined by u, v and w?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.