Find the Flux of the Vector Field F Across the Surface

question 92

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } ( x , y , z ) = x z i + y z j + k , S$ is the cap cut from the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ by the plane $z = 3$ , direction is outward

• A) \(\frac { 63 } { 2 } \pi\)
• B) \(- \frac { 63 } { 2 } \pi\)
• C) \(\frac { 35 } { 2 } \pi\)
• D) \(63 \pi\)

---

Definitions:

Balanced Scorecard

A strategic planning and management system used by organizations to communicate what they are trying to accomplish and to measure and monitor progress towards strategic targets.

Organizational Performance

A measure of how effectively and efficiently an organization meets its goals and objectives.

Internal Processes

Refers to the procedures and operations that take place within an organization to ensure its smooth and effective functioning.

Ethics Auditing Process

A systematic evaluation of an organization's ethical policies and practices, aimed at identifying strengths and weaknesses and proposing improvements.