/*! 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. Let v聽=聽a,聽b,聽c and w聽=聽伪... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 5. (page 845)

Let v=a,b,c and w=伪,尾,纬 where v and w are not parallel vectors. Explain why the planes ax+by+cz=d and 伪x+尾y+纬z=未 intersect.

Short Answer

Expert verified

The planes ax+by+cz=d and 伪x+尾y+纬z=未 intersect.

Step by step solution

01

Given information

Consider the vectors v=鉄�a,b,c鉄� and w=鉄�伪,尾,纬鉄� which are not parallel

02

Calculation

The objective is to explain why the planes ax+by+cz=dand 伪x+尾y+纬z=未intersect.

Use the finding that lines in a plane either intersect or are parallel to each other to explain why the planes intersect.

The vectors v=鉄�a,b,c鉄� and w=鉄�伪,尾,纬鉄� normal to the two planes are not parallel. Therefore, they must intersect.

Therefore, the planes ax+by+cz=d and 伪x+尾y+纬z=未 intersect.

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 PQ鈫�

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

Give an example of three nonzero vectors u, v and w in 鈩�3 such that u脳v=u脳w but v鈮�w. What geometric relationship must the three vectors have for this to happen?

Find the norm of the vector.v=3,鈭�4

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

u=-5,1,3,v=-3,2,7

In Exercises 30鈥�35 compute the indicated quantities when

u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

u脳vandv脳u
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.