Prove the following identities using tensor (index) notations. (A x B) (A x B) = AB...

 

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Prove the following identities using tensor (index) notations. (A x B) (A x B) = AB - (AB), V(A B) = A x (V x B) + Bx (V x A) + (AV)B + (B. V)A, . B. Use index (tensor) notations to calculate: the following: (a) (b) (c) (d) (e) V(r/r), (f) V{(3r,rk-r8jk)/r5} and, (g) Virj, V.r, Vr, Vrk where k is rational, Veikr where k is a constant vector. Prove the following identities using tensor (index) notations. (A x B) (A x B) = AB - (AB), V(A B) = A x (V x B) + Bx (V x A) + (AV)B + (B. V)A, . B. Use index (tensor) notations to calculate: the following: (a) (b) (c) (d) (e) V(r/r), (f) V{(3r,rk-r8jk)/r5} and, (g) Virj, V.r, Vr, Vrk where k is rational, Veikr where k is a constant vector.

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Sure Lets use tensor index notation to prove the given identities and calculate the expressions a To ... View the full answer