/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q22P Square (A聽+聽B); interpret your... [FREE SOLUTION] | 91影视

91影视

Log out

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+2A脳B.

Step by step solution

01

Concept and formula used

Using the formula,

(A+B)2=(A+B)脳(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)脳(A+B)=|A|2+A脳B+B脳A+|B|2=|A|2+2A脳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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

In a parallelogram, the two lines from one corner to the midpoints of the two opposite sides trisect the diagonal they cross.

Are the following linear vector functions? Prove your conclusions using (7.2).

4.F(r)=r+A,whereAis a given vector.

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=12(12-12021-2-1)

Prove the following by appropriate manipulations using Facts 1 to 4; do not just evaluate the determinants.

|1abc1bac1cab|=|1aa21bb21cc2|=(c-a)(b-a)(c-b)|1aa201b+a001|=(c-a)(b-a)(c-b)

To see a physical example of non-commuting rotations, do the following experiment. Put a book on your desk and imagine a set of rectangular axes with the xand yaxes in the plane of the desk with the zaxis vertical. Place the book in the first quadrant with the x and yaxes along the edges of the book. Rotate the book90掳about the xaxis and then90掳about theaxis; note its position. Now repeat the experiment, this time rotating90掳about theaxis first, and then90掳about the xaxis; note the different result. Write the matrices representing the90掳rotations and multiply them in both orders. In each case, find the axis and angle of rotation.

For each of the following matrices, find its determinant to see whether it produces a rotation or a reflection. If a rotation, find the axis and angle of rotation. If a reflection, find the reflecting plane and the rotation (if any) about the normal to this plane.
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Rotational Dynamics

Read Explanation

Nuclear Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Waves Physics

Read Explanation

Thermodynamics

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.