Show that (i) ∇. (A × B⃗ ) = B⃗ . (∇ × A ) − A . (∇ × B⃗ ) (ii) ∇(A . B⃗ ) = (B⃗ . ∇)A + (A . ∇)B⃗ + B⃗ × (∇ × A ) + A × (∇ × B⃗ ).. Created by claryn.

Show that (i) ∇. (A × B⃗ ) = B⃗ . (∇ × A ) − A . (∇ × B⃗ ) (ii) ∇(A . B⃗

July 2023 1 4 Report

Show that (i) ∇. (A × B⃗ ) = B⃗ . (∇ × A ) − A . (∇ × B⃗ ) (ii) ∇(A . B⃗ ) = (B⃗ . ∇)A +
(A . ∇)B⃗ + B⃗ × (∇ × A ) + A × (∇ × B⃗ ).