Find the Flux $\vec { F }$ Of Through $S$ $\iint _ { S } \vec { F } \cdot \vec { N } d S$

question 37

Multiple Choice

Find the flux $\vec { F }$ of through $S$ , $\iint _ { S } \vec { F } \cdot \vec { N } d S$ , where $\vec { N }$ is the upward unit normal vector to S. $\overrightarrow { \mathbf { F } } ( x , y , z ) = 2 z \hat { \mathbf { i } } - 8 \hat { \mathbf { j } } + y \hat { \mathbf { k } }$
$S : x + y + z = 9$ , first octant

• A) \(- \frac { 81 } { 2 }\)
• B) \(\frac { 81 } { 2 }\)
• C) \(\frac { 99 } { 2 }\)
• D) \(\frac { 93 } { 2 }\)
• E) \(- \frac { 87 } { 2 }\)

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Definitions:

Schizotypal Personality Disorder

A mental disorder characterized by severe social anxiety, thought disorder, paranoid ideation, derealization, transient psychosis, and often unconventional beliefs.

Ideas Of Reference

A cognitive distortion where individuals falsely believe that unrelated events or actions of others are specifically related to them.

Bodily Illusions

False perceptions or misinterpretations of one’s own body parts or bodily sensations.

Antisocial Personality Disorder

Antisocial Personality Disorder is a mental health condition characterized by a long-term pattern of manipulating, exploiting, or violating the rights of others.