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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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7

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Vector algebra

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7.1  Which of the following statements about general vectors a, b and c are true?

(a)  c · (a × b) = (b × a) · c;

(b)  a × (b × c) = (a × b) × c;

(c)  a × (b × c) = (a · c)b − (a · b)c;

(d)  d = λa + μb implies (a × b) · d = 0;

(e)  a × c = b × c implies c · ac · b = c |ab|;

(f)  (a × b) × (c × b) = b[ b · (c × a)].

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All of the tests below are made using combinations of the common properties of the various types of vector products ...

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