Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Suppose that all sides of a quadrilateral are equ…

05:13

Question

Answered step-by-step

Problem 59 Hard Difficulty

Prove Properties 2, 4, and 5 of the dot product (Theorem 2).


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

WZ
Wen Zheng
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Related Topics

Vectors

Discussion

You must be signed in to discuss.
Top Calculus 3 Educators
Lily An

Johns Hopkins University

Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Joseph Lentino

Boston College

Calculus 3 Courses

Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

Join Course
Recommended Videos

03:52

Prove Properties $2,4,$ an…

01:35

Prove Property 4 of the do…

Watch More Solved Questions in Chapter 12

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65

Video Transcript

The problem is proof properties, 24 and 5 of the dot product property 2 is a dot b, is equal to b dot a here we can let a is equal to a 1 a 2. A 3 point b is equal to e o b 2 b 3. So a dot b is equal to a 1 b 1 plus a 2 b 2 plus a 3 b, 3 and b dot a is equal to v, 1, a 1 plus b 2, a 2 plus 8 e 3 a 3. So this is equal to a 1 b 1 plus a 2 v 2 plus 3 b 3 s. This is equal to a dot b. Property 4 is scattered c times. A dot b is equal to scatter c times. A dot b is equal to a dot square c times b, so first to reprove this equation, and similarly we can prove another equation: a is equal to c a 1 c, a 2 c, a 3 point. So c, a dot b is equal to c, a 1 b, 1 plus c, a 2 b, 2 plus c 83 b 3 point. So this is equal to c times a 1 b, 1 plus a 2 b, 2 plus 83 b 3 point. So this is equal to s times a dot b. To similarly become proof. The other equation- property 5- is 0 dot. A is equal to 00 is a vector, 000 point, so 0 dot a is equal to 0 times a 1 plus 0 times a 2 plus 0 times a 3 point. So this is equal to 0.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
180
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
79
Hosted by: Alonso M
See More

Related Topics

Vectors

Top Calculus 3 Educators
Lily An

Johns Hopkins University

Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Joseph Lentino

Boston College

Calculus 3 Courses

Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

Join Course
Recommended Videos

03:52

Prove Properties $2,4,$ and 5 of the dot product (Theorem 2$)$

01:35

Prove Property 4 of the dot product. Use either the definition of a dot product…
Additional Mathematics Questions

02:16

number of four digit numbers with all digits different and containing the di…

02:08

P is point out side the circle. If the farthest distance of P from the circl…

00:56

The dimensions of a cuboidal iron slab are 1.5m × 25cm × 150cm . Find its vo…

05:57

The height of a hill is 3,300 metres. From the point D on the ground the ang…

03:06

A box contains 5 radio tubes of which 2 are defective.The tubes are tested o…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started