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Chapter 10: Q5P (page 502)

Write equations (2.12) out in detail and solve the three simultaneous equations (say by determinants) forx1,x2,x3in terms ofx1',x2',x3'to verify equations (2.13) . Use your results in Problem 4.

Short Answer

Expert verified

The statement has been verified.

Step by step solution

01

Given Information

In matrix A, each element is the component of vectors.

02

Definition of Orthonormal triad.

The Orthonormal vector triad is the unit vectors in the positive direction of the three mutually perpendicular axes.

03

Show that Column vectors of A are orthonormal.

In matrix A, each element is the component of vectors.

The formula for the cartesian vectors states that Vi'=鈭�j=13aijVj

In matrix form it is written asV'=A蟿V

Since, A is an orthogonal matrix.

A蟿V'=AATVA蟿V'=IVA蟿V'=V

The equation becomes as follows

Vi'=鈭�j=13A蟿ijV'jVi'=鈭�j=13aijV'j

Hence The statement has been verified.

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