Question: detailed steps Problem 2: Using index notation, demonstrate mathematically the following equations: 1- uxv= -vxu 2- V.(Va) = Va 3- V? (ab) = aVb+ 2Va

detailed steps

Problem 2: Using index notation, demonstrate mathematically the following equations: 1- uxv= -vxu 2- V.(Va) = Va 3- V? (ab) = aVb+ 2Va . Vb+bV2a 4- V . (ab ) = Va . btaV .b 5- VxVo =0 6- V . ( V X V ) = 0 7- V .V # V . V (express each term in index notation and expand in Cartesian coordinates to prove the inequality) 8- (axb) . (cxd) = (a .c) (b .d) -(a .d)(b .c)

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