Question

Consider the statements.
I. If \(f\) is a differentiable scalar field, then \(curl(grad\, f) = \vec{0\).
II. If \(\vec{f}\) is a differentiable vector field, then \(div(curl\, \vec{f}) = 0\).
Which one of the following is correct?

• A. I is true, but II is false
• B. I is false, but II is true
• C. Both I and II are true
• D. Neither I nor II is true

Hint:

Remember two fundamental rules of vector calculus:
1. The curl of any gradient field is always zero ($\nabla \times \nabla f = \vec{0}$).
2. The divergence of any curl field is always zero ($\nabla \cdot (\nabla \times \vec{f}) = 0$).

Answer 1

The Correct Option is C