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? is a vector field and ? is a scalar field 1. Prove in 3 dimensions:...

? is a vector field and ? is a scalar field

1. Prove in 3 dimensions: ∇ ∙ (∇ × ? ) = 0

2. Prove in 3 dimensions: ∇ × (∇φ) = 0

3. Prove in 3 dimensions: (?∙∇) ?= −? × (∇ × ?)+ ∇((?∙?)/ 2)

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