/*! 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} Q. 38 Show that the projection of v聽o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 38 (page 613)

Show that the projection of vonto iis v路ii. Then show that we can always write a vector vas

v=(v路i)i+(v路j)j

Short Answer

Expert verified

Yes, the projection ofvontoiisv路iiand the vectorvisv路ii+v路jj.

Step by step solution

01

Step 1. Given Information

We have to show that the projection of vonto iisv路iiand vectorvisv路ii+v路jj.

02

Step 2. Showing the projection of v onto i

As we know If vand ware two nonzero vectors, the vector projection of vonto w is

v1=v路ww2w

iis the unit vector, so the projection of vonto iis

role="math" localid="1646824336209" v1=v路ii2iv1=v路iii2=1..........(a)

Hence proved that the projection ofvontoiisv路ii.

03

Step 3. Showing the vector v

We have found the projection of vonto i,now let's find the projection of vonto j.

jis the unit vector so,

v2=v路jj2jv2=v路jjj2=1.........(b)

We can write vector vas

v=v1+v2v=v路ii+v路jj

Hence proved.

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

find the unit vector in the same direction as v

v=-3j

v=-3j

Match the graph with the polar equation.

r=2sin胃

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

-1,0

Find zw and zw. Leave the answers in polar form.

z=1-iw=1-3i

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

r=4
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

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.