Chapter 1: Q52P (page 55)
For Theorem 2, show that , , , and
Short Answer
The statement has been shown. The statements localid="1653024780843" and has been shown. The statement has been shown.
Chapter 1: Q52P (page 55)
For Theorem 2, show that , , , and
The statement has been shown. The statements localid="1653024780843" and has been shown. The statement has been shown.
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Get started for freeLet be the separation vector from a fixed point to the point localid="1654317524404" , and let r be its length. Show that
(a)localid="1654317730952"
(b)
(c) What is the general formula for localid="1654317981268"
Find the angle between the body diagonals of a cube.
For Theorem 2, show that
(a) How do the components of a vectoii transform under a translationof coordinates (X= x, y= y- a, z= z,Fig. 1.16a)?
(b) How do the components of a vector transform under an inversionof coordinates (X= -x, y= -y, z= -z,Fig. 1.16b)?
(c) How do the components of a cross product (Eq. 1.13) transform under inversion? [The cross-product of two vectors is properly called a pseudovectorbecause of this "anomalous" behavior.] Is the cross product of two pseudovectors a vector, or a pseudovector? Name two pseudovector quantities in classical mechanics.
(d) How does the scalar triple product of three vectors transform under inversions? (Such an object is called a pseudoscalar.)
(a) Find the divergence of the function
(b) Find the curlof .Test your conclusion using Prob. 1.61b. [Answer:]
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