Find the Correct Identity, If $f$ Is a Scalar Field $\mathbf { F }$

question 108

Multiple Choice

Find the correct identity, if $f$ is a scalar field, $\mathbf { F }$ and $\mathbf { G }$ are vector fields.

• A) \(\operatorname { div } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f\)
• B) \(\quad \operatorname { curl } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f\)
• C) \(\operatorname { div } ( f \mathbf { F } ) = f \operatorname { curl } ( \mathbf { F } ) + ( \nabla f ) \times \mathbf { F }\)
• D) None of these

---

Definitions:

Average Tax Rate

The fraction of total income that is paid in taxes, calculated by dividing the total amount of taxes paid by the taxpayer's total income.

Legal Obligation

A requirement by law for an individual or entity to follow certain conduct or make certain payments.

Balance Budget

A financial plan or policy where total revenues are equal to or greater than total expenditures.

Tax Receipts

The total amount of money received by the government from taxes, serving as a primary source of revenue.