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Q. 6

Expert-verified

Calculus

Found in: Page 823

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

What is Lagrange’s identity? How is it used to understand the geometry of the cross product?

A relationship between the dot product and cross product and help us understand the geometry of the cross product is known as Lagrange’s identity.

It is used to understand the geometry of the cross product as ${||u \times v||}^{2} = {||u||}^{2} {||v||}^{2} - {(u \cdot v)}^{2}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

We have to explain what is Lagrange’s identity and how is it used to understand the geometry of the cross product.

Step 2. The Lagrange’s identity

A relationship between the dot product and cross product and will be used shortly to help us understand the geometry of the cross product. It is known as Lagrange’s identity

Step 3. It is used to understand the geometry of the cross product as

Let u and v be vectors in $ℝ^{3}$ . Then

${||u \times v||}^{2} = {||u||}^{2} {||v||}^{2} - {(u \cdot v)}^{2}$

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