Dynamics_Part3

Dynamics_Part3 - Problem Set 1 Problem 3 Problem Verify...

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Problem Set 1: Problem 3. Problem: Verify that ( A × B ) · C =( C × A ) · B B × C ) · A holds for the three vectors A = a ( i + j ) , B = b ( i + j ) and C = c ( i + k ) . Solution: In order to verify the vector identity for the three specified vectors, we proceed term by term. So, concentrating first on ( A × B ) · C ,wehave A × B = e e e e e e e ijk aa 0 bb 0 e e e e e e e =(0 0) i (0 0) j +[( ab ( ab )] k =2 ab k Thus, ( A × B ) · C ab k · c ( i + k )=2 abc Turning now to ( C × A ) · B ,weob ta in C × A = e e e e e e e c 0 c 0 e e e e e e e ac ) i (0 ac ) j +( ac 0) k = ac ( i + j + k ) so that, ( C × A ) · B = ac ( i + j + k ) · b ( i + j abc Finally, for ( B × C ) · A , there follows B × C = e e e
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