Divergence of Curl Identity

Correct Answer

D — Both statements 1 and 2 are true

Statement-wise Analysis

Statement 1: True

Statement 2: True

Concept and Reasoning

The curl of a vector field is itself a vector field. In any sufficiently smooth field, the vector identity ∇·(∇×A)=0 holds identically. Therefore both statements are correct and option D applies.

Calculation / Key Relation

∇·(∇×A)=0

Exam Takeaway

Divergence of any curl is zero.

Common Mistake

Do not confuse this identity with curl of a gradient, ∇×(∇V)=0; both are valid but different identities.