Question

Which of the following are true:
A. $\text{div }(\vec{F} \times \vec{G}) = \vec{G} \cdot \text{curl } \vec{F} - \vec{F} \cdot \text{curl } \vec{G}$ B. $\text{div }(\text{curl } \vec{F}) = 0$ C. $\text{curl }(\vec{\nabla} f) = 0$ D. $\text{div }(\vec{\nabla} f \times \vec{\nabla} g) \neq 0$ E. $\vec{\nabla}(fg) = f \vec{\nabla} g + g \vec{\nabla} f$ Choose the correct answer from the options given below:

• A. A, B, C, D, E
• B. A, B, C Only
• C. A, B, C, E Only
• D. A, B, E Only

Hint:

Two famous null identities in vector calculus: 1. $\text{div}(\text{curl } \vec{A}) = 0$ 2. $\text{curl}(\text{grad } f) = \vec{0}$

Answer 1

The Correct Option is C