Find the Correct Identity, If F Is a Scalar Field $\operatorname { div } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f$

question 35

Multiple Choice

Find the correct identity, if f is a scalar field, F and G are vector fields.

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

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Definitions:

Correlation Coefficients

Statistical measures that quantify the degree to which two variables are related or move together, ranging from -1 to +1.

Correlation Coefficient

A numerical indicator that shows the degree to which two or more variables move in conjunction with each other.

Negative Correlation

A relationship between two variables where one variable increases as the other decreases, indicating an inverse relationship.

Negative Correlation

A bond between two factors where as one escalates, the other diminishes.