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 12 (page 801)

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Expert verified

The required vector is: $<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}>$

Step by step solution

Given information

Given a vector $<a, b, c>$

Finding the vector

The vector is in opposite direction so negative sign has to be applied and half means multiplying the vector with scalar $\frac{1}{2}$ .

The required vector is:

$<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}> .$

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

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is $k = 1$ .

(b) True or False: $\sum_{k = 0}^{n} \frac{1}{k + 1} + \sum_{k = 1}^{n} k^{2}$ is equal to $\sum_{k = 0}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(c) True or False: $\sum_{k = 1}^{n} \frac{1}{k + 1} + \sum_{k = 0}^{n} k^{2}$ is equal to $\sum_{k = 1}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(d) True or False: $(\sum_{k = 1}^{n} \frac{1}{k + 1}) (\sum_{k = 1}^{n} k^{2})$ is equal to $\sum_{k = 1}^{n} \frac{k^{2}}{k + 1}$ .

(e) True or False: $\sum_{k = 0}^{m} \sqrt{k} + \sum_{k = m}^{n} \sqrt{k}$ is equal to $\sum_{k = 0}^{n} \sqrt{k}$ .

(f) True or False: $\sum_{k = 0}^{n} a_{k} = - a_{0} - a_{n} + \sum_{k = 1}^{n - 1} a_{k}$ .

(g) True or False: ${(\sum_{k = 1}^{10} a_{k})}^{2} = \sum_{k = 1}^{10} a_{k}^{2}$ .

(h) True or False: $\sum_{k = 1}^{n} {(e^{x})}^{2} = \frac{e^{x} (e^{x} + 1) (2 e^{x} + 1)}{6}$ .

If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

role="math" localid="1649603943715" $u = (3, 6, 11) a n d v = (1, - 2, 3)$

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

Find the area of the parallelogram determined by the vectors u and v.

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <2, 1, - 5>$

See all solutions

Recommended explanations on Math Textbooks

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

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Company

Product

Help

Find a vector parallel to a,b,cbut half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.