Chapter 9: Q. 46 (page 603)

Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| + ||w||$

Short Answer

Expert verified

The quantity of $||v|| + ||w||$ is $\sqrt{34} + \sqrt{13}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$v = 3 i - 5 j w = - 2 i + 3 j$

The magnitude of the vector $v = a_{1} i + b_{1} j$ ,

$||v|| = \sqrt{{(a_{1})}^{2} + {(b_{1})}^{2}}$

Compare $v = 3 i - 5 j$ with the standard form $v = a_{1} i + b_{1} j$ ,

$a_{1} = 3, b_{1} = - 5$

Then,

$||v|| = \sqrt{{(3)}^{2} + {(- 5)}^{2}} ||v|| = \sqrt{9 + 25} ||v|| = \sqrt{34}$

Step 2. Compare w with the standard form.

Compare $w = - 2 i + 3 j$ with the standard form $v = a_{1} i + b_{1} j$ ,

$a_{1} = - 2 b_{1} = 3$

Then,

$||w|| = \sqrt{{(- 2)}^{2} + 3^{2}} ||w|| = \sqrt{4 + 9} ||w|| = \sqrt{13}$

Therefore, we can write,

$||v|| + ||w|| = \sqrt{34} + \sqrt{13}$

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| + ||w||$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare w with the standard form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Geometry

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find each quantity if v=3i-5j,w=-2i+3j.v+w

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare w with the standard form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Geometry

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| + ||w||$