Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 10: Q 47. (page 801)

Find a vector in the direction opposite to-1,-4,-6andwith magnitude 7.

Short Answer

Expert verified

The required vector is7531,4,6.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=-1,-4,-6 with magnitude 7.

02

Step 2. Find the norm of the vector.

v=-1,-4,-6v=-12+-42+-62=1+16+36=53

Therefore, the norm of the given vector is 53.

03

Step 3. Find the vector.

We know that the vector in the direction of vis av-v. Here ais the magnitude of the given vector and the negative sign shows the direction opposite to v=-1,-4,-6.

The required vector is:

av-v=753--1,-4,-6=7531,4,6


Therefore the vector in the direction opposite tov=-1,-4,-6and with a magnitude of 7 is 7531,4,6.

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

Use the Intermediate Value Theorem to prove that every cubic function f(x)=Ax3+Bx2+Cx+Dhas at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

In Exercises 36–41 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,−2),Q(−2,0),R(1,−5)

(Hint: Think of the xy-plane as part of ℝ3.)

Find a vector in the direction of 9,0,-6and with magnitude 7.

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

u×vandv×u

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

Find the area of the parallelogram determined by the vectors v and w.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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