Problem 4 Using Levi-Civita symbol, show that ? × (A × B) = (B · ?)A ? (A · ?)B + A(? · B) ? B(? · A). Problem 5 Using Levi-Civita symbol, show that ? · (? × A) = 0. Problem 6 Using Levi-Civita symbol, show that ? × (? × A) = ?(? · A) ? ?²A.
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We know that the cross product can be expressed using the Levi-Civita symbol as follows: $(V \times (A \times B))_i = \epsilon_{ijk} V_j (A \times B)_k$ Now, we can expand $(A \times B)_k$ using the Levi-Civita symbol as well: $(A \times B)_k = \epsilon_{klm} Show more…
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