Mathematics · Vector Calculus
Which of the following identities of vector calculus is correct for differentiable vector fields f, g and scalar field φ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1∇ × (∇ × f) = ∇(∇ · f) + ∇2f
- 2∇ · (f × g) = g · (∇ × f) − f · (∇ × g)✓
- 3∇ · (φf) = φ(∇ · f) − f · (∇φ)
- 4∇ × (∇φ) ≠ 0
Correct answer
∇ · (f × g) = g · (∇ × f) − f · (∇ × g)
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