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PS1-3 - Problem Set 1 Problem 3 Problem Verify that(A B C...

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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 + 2 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 , we have A × B = e e e e e e e i j k 1 2 2 2 1 1 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 i j k 4 3 5 1 2 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 , we obtain A · C = ( i 2 j + 2 k ) · ( i + 2 j k ) = 1 4 2 = 5 B · C = (2 i + j + k ) · ( i + 2 j
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