Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: 22 P (page 137)

Question: Find a condition for the three lines in a plane to intersect in one point. Hint:See Problem. Write the equation of a line asax+by=c. Assume that no two of the lines are parallel.

Short Answer

Expert verified

The condition for the three lines in a plane to intersect at one point is that the determinant of the coefficient should be zero.

a1b1c1a2b2c2a3b3c3=0

Step by step solution

01

Definition of plane

A plane is defined as a flat, two-dimensional surface that extends indefinitely in mathematics. Also, the two-dimensional equivalence of a point, a line, and three-dimensional space is considered a plane.

02

Finding a condition for the three lines in a plane that intersect at one point

The given equation isax+by=c.

Consider the three lines and their equation as

a1x+b2y=c1a2x+b2y=c2a3x+b3y=c3

The above system of equations should have a solution that can satisfy the three equations for these three lines to intersect.

This implies that the above three equations have been linearly dependent.

Thus, the condition is that the determination of the coefficient should be zero.

a1b1c1a2b2c2a3b3c3=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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Verify the details as indicated in diagonalizing H in (11.29).

Find AB, BA , A+B , A-B , A2, B2,5.A,3,B . Observe that AB≠BA. Show that (A-B)(A+B)≠(A+B)(A-B)≠A2-B2. Show that det(AB)=det(BA)=(detA)(detB), but that det(A+B)≠detA+detB. Show that det(5A)≠5detA and find n so that det(5A)=5ndetA. Find similar results for det(3B). Remember that the point of doing these simple problems by hand is to learn how to manipulate determinants and matrices correctly. Check your answers by computer.

role="math" localid="1658986967380" A=(1023-10051),B=(1100213-10)


For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint: Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using.

7.

If A=4i-3k and B=-2i+2j-k,find the scalar projection of A on B the scalar projection of B on A,and the cosine of the angle between A and B .

Question: For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using

6.{x+y-z=13x+2y-2z=3
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Thermodynamics

Read Explanation

Solid State Physics

Read Explanation

Linear Momentum

Read Explanation

Wave Optics

Read Explanation

Space 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.

Sign-up for free