PS1-3 - Problem Set 1: Problem 3. Problem: Verify that (A...

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Problem Set 1: Problem 3. Problem: Verify that ( A × B ) × C =( A · C ) B ( B · C ) A for the three vectors A = i 2 j +2 k , B =2 i + j + k and C = i j 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 1 22 211 e e e e e e e 2 2) i (1 4) j +[1 ( 4)] k = 4 i +3 j +5 k Thus, ( A × B ) × C = e e e e e e e ij k 435 12 1 e e e e e e e 3 10) i (4 5) j +( 8 3) k = 13 i + j 11 k Turning now to ( A · C ) B ( B · C ) A ,weob ta in A · C i 2 j k ) · ( i j k )=1 4 2= 5 B · C 2 i + j + k ) · ( i j k )=2+2 1=3 Finally, we conclude that
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This note was uploaded on 10/12/2009 for the course AME 301 at USC.

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