/*! 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. 57 In Problems 51鈥�58, find the do... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 57 (page 622)

In Problems 51鈥�58, find the dot product v.w and the angle between v and w.

v=3i+4j+k;w=6i+8j+2k

Short Answer

Expert verified

The dot product of the vectors

v=3i+4j+k;w=6i+8j+2k

is 52 and the angle between them is 0.

Step by step solution

01

Step 1. Given

The vectors:

v=3i+4j+k;w=6i+8j+2k

To find the dot product and the angle between them.

02

Step 2. Dot product of the vectors.

The dot product is given by,

v.w=(3i+4j+k).(6i+8j+2k)=(3)(6)+(4)(8)+(1)(2)=52

03

Step 3. Angle between the vectors.

If u and v are two nonzero vectors, the angle胃,0鈮�胃鈮�蟺between u and v is determined by the formula,cos胃=u.vuv

04

Step 4. Find the length of the vectors.

Now,

v=3i+4j+k=32+42+(1)2=26

w=i+2j+2k=62+82+22=104

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=5226104=5252胃=cos-1(1)=0

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 each quantity if v=3i-5jand w=-2i+3j

v+w

Identify and graph each polar equation. Verify your graph using a graphing utility.
r=2+4cos胃

Use the figure at the right. Determine whether the given statement is true or false.

K+G=F

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

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

-1,0
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

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.