Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

Chapter 3: Q22P (page 105)

Square $(A + B)$ ; interpret your result geometrically. Hint: Your answer is a law which you learned in trigonometry.

Short Answer

Expert verified

The law of cosine $| A |^{2} + | B |^{2} + 2 A \times B$ .

Step by step solution

01

Concept and formula used

Using the formula,

$(A + B)^{2} = (A + B) \times (A + B)$

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

02

Step 2: Using the trigonometric law

Squaring $(A + B)$ ,

$(A + B)^{2} = (A + B) \times (A + B) = | A |^{2} + A \times B + B \times A + | B |^{2} = | A |^{2} + 2 A \times B + | B |^{2}$

This is law of cosine.

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

Question: Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.

$(\begin{matrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{matrix})$

A particle is traveling along the line (x-3)/2=(y+1)/(-2)=z-1. Write the equation of its path in the form $r = r_{0} + At$ . Find the distance of closest approach of the particle to the origin (that is, the distance from the origin to the line). If t represents time, show that the time of closest approach is $t = - (r_{0} \times A) / {| A |}^{2}$ . Use this value to check your answer for the distance of closest approach. Hint: See Figure 5.3. If P is the point of closest approach, what is $A \times r^{2}$ ?

Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer

$(\begin{matrix} - 1 & 2 & 1 \\ 2 & 3 & 0 \\ 1 & 0 & 3 \end{matrix})$

Show that each of the following matrices is orthogonal and find the rotation and/or reflection it produces as an operator acting on vectors. If a rotation, find the axis and angle; if a reflection, find the reflecting plane and the rotation, if any, about the normal to that plane.

$M = \frac{1}{2} (\begin{matrix} 1 & \sqrt{2} & - 1 \\ \sqrt{2} & 0 & \sqrt{2} \\ 1 & - \sqrt{2} & - 1 \end{matrix})$

Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.

$(\begin{matrix} 2 & 2 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & - 1 \end{matrix})$

See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Dynamics

Read Explanation

Torque and Rotational Motion

Read Explanation

Radiation

Read Explanation

Engineering 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