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Chapter 10: Q18P (page 496)

Using (10.19), show that ai aj =𝛿 i j.

Short Answer

Expert verified

The equation has been proven.

Step by step solution

01

Given Information:

The directions of the vectors ai, aj .

02

Definition of covariant basis vector:

A covariant vector, also known as a cotangent vector, has components that co-vary when the basis changes. That is, the components must be converted using the same matrix as the base matrix change.

03

Find the value:

The value of ai , aj are mentioned below.

Apply chain rule in the above equation, the equation becomes as follows.

Hence, the equation has been proven.

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Most popular questions from this chapter

∂B∂t=-∇×E

P Derive the expression (9.11)for curl V in the following way. Show that ∇x1=e1h1 and ∇×(∇x1)=∇×(e1h1)=0 . Write V in the form V=e1h1(h1V1)+e2h2(h2V2)+e3h3(h3V3)and use vector identities from Chapter 6 to complete the derivation.

Parabolic cylinder.

In equation(5.12) , find whetherA×(B×C) is a vector or a pseudovector assuming

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Hint: Count up the number of det A factors from pseudovectors and cross products.

XiAj=Bij.
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