Find the Flux of the Vector Field F Across the Surface

question 197

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = 12 \mathrm { x } + 12 \mathrm { y } \mathbf { j } + 12 \mathrm { z } \mathbf { k } , \mathrm { S }$ is the surface of the sphere $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 1$ in the first octant, direction away from the origin

• A) \(4 \pi\)
• B) \(6 \pi\)
• C) \(3 \pi\)
• D) 0

---

Definitions:

Cross-Cultural

Pertaining to or comparing two or more different cultures, often emphasizing the interaction and comparative study of their differences and similarities.

Cross-Border Mergers

Transactions where companies from different countries combine their operations or assets, often to expand market reach or consolidate industry positions.

Direct Foreign Investment

A financial commitment by an individual or company from one country into business ventures or assets in another country, whether by setting up business activities or purchasing business assets.

Export Cooperatives

Organizations formed by producers with the aim of marketing and selling their products in foreign markets collectively.