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Chapter 10: Q18P (page 496)

Using (10.19), show that ai aj =饾浛 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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