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

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

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

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.

Problem

Suppose that all sides of a quadrilateral are equ…

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

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Lily An

Catherine Ross

Kayleah Tsai

Joseph Lentino

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

James Stewart

Calculus: Early Transcendentals

Lily An

Catherine Ross

Kayleah Tsai

Joseph Lentino

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

Calculus: Early Transcendentals

Lily An

Catherine Ross

Kayleah Tsai

Joseph Lentino

James StewartCalculus: Early Transcendentals

Lily An

Catherine Ross

Kayleah Tsai

Joseph Lentino

James Stewart

Calculus: Early Transcendentals