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Chapter 10: Q. 6 (page 823)

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

Short Answer

Expert verified

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

It is used to understand the geometry of the cross product asu脳v2=u2v2鈭�(u路v)2.

Step by step solution

01

Step 1. Given Information 

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

02

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鈥檚 identity

03

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

Let u and v be vectors in 鈩�3. Then

u脳v2=u2v2鈭�(u路v)2

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