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Problem

Prove the property of cross products (Theorem 11)…

04:37

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Problem 22 Easy Difficulty

Show that $ (a \times b) \cdot b = 0 $ for all vectors $ a $ and $ b $ in $ V_3 $.


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WZ

Wen Zheng

Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Related Topics

Vectors

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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.

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Watch More Solved Questions in Chapter 12

Problem 1
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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

Video Transcript

Welcome back to another cross product problem where we're going to try and find the value of a cross B dot be for any vectors, A and B. So A can be any value, can be can be any value. Now, there's a couple different ways we can try this. The naive way would be to plug in a one, A two, A three, B one B two In B three in our matrix. And then use the method in the textbook, calculating the cross product of each combination of these and then take that vector and doubt it with B. But instead, let's use properties of cross products that tells us a Crosby dot another vector. It's the same thing as a God be cross that other vector. This problem is a lot easier to figure out because B Crosby is a vector cross product itself. And we know that any time we have a vector cross product itself, or a vector cross product, something parallel to itself, That's just zero. Meaning this problem reduces to Calculating a.0 or a one a two a three dot product with 000 Which is just zero times a one Plus zero times a two Plus zero times a three for just zero. If we did all the math, the slow way would give us the exact same result, but it would take a lot longer to get better. Even your time. Thanks for watching.

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Calculus: Early Transcendentals

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Related Topics

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Top Calculus 3 Educators
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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
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