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Q. 6

Expert-verified
Found in: Page 823

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# 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 ${||u×v||}^{2}={||u||}^{2}{||v||}^{2}-{\left(u·v\right)}^{2}$.

See the step by step solution

## 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 ${\mathrm{ℝ}}^{3}$. Then

${||u×v||}^{2}={||u||}^{2}{||v||}^{2}-{\left(u·v\right)}^{2}$