solns7 - (f) Cross product is not associative (see (d)),...

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Unformatted text preview: (f) Cross product is not associative (see (d)), has no identity and no inverse. 2. Since (Mi)jk = -εijk , [ M i , M j ] mn = ( M i ) mk ( M j ) kn − ( M j ) mk ( M i ) kn = ε imk ε jkn − ε jmk ε ikn = −ε imk ε jnk + ε jmk ε ink = − (δ ij δ mn − δ in δ jm ) + δ ji δ mn − δ jn δ mi = δ in δ jm − δ jn δ mi ε ijk ( M k ) mn = ε ijk ( − ε kmn ) = − (δ im δ jn − δ in δ jm ) ...
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This note was uploaded on 11/16/2010 for the course PHY 504 taught by Professor Staff during the Fall '08 term at Kentucky.

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