/*! 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 22. In Exercises 20-23, find the dot... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 22. (page 812)

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=3,-1,2,v=-4,-6,3

Short Answer

Expert verified

The dot product is 0 and the angle is90掳.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=3,-1,2,v=-4,-6,3

02

Step 2. Find the dot product.

The dot product is:u路v=u1v1+u2v2+u3v3

u=3,-1,2andv=-4,-6,3u路v=3-4+-1-6+23=-12+6+6=0

Therefore, the dot product of the given two vectors u=3,-1,2andv=-4,-6,3is 0.

03

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

cos胃=u.vuvu=3,-1,2andv=-4,-6,3u路v=0u=32+-12+229+1+4=14v=-42+-62+3216+36+9=61

Then,

cos胃=u.vuvcos胃=01461cos胃=0胃=cos-10=90掳

Therefore, the angle is90掳.

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 a vector in the direction of -1,2,3with magnitude 3.

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [鈭�4, 4], and illustrate this average value as a height on the graph.

How is the determinant of a 3 脳 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3)?

Find PQ鈫�

P=-1,5,4,Q=-1,6,4

If u and v are nonzero vectors in 鈩�3, what is the geometric relationship between u,v and u脳v?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.