Test the Vector Field F to Determine If It Is

question 267

Multiple Choice

Test the vector field F to determine if it is conservative.
- $$\mathrm { F } = 7 \mathrm { x } ^ { 7 } \mathrm { y } ^ { 5 } \mathrm { i } + \left( 5 \mathrm { x } ^ { 7 } \mathrm { y } ^ { 4 } + \frac { \mathrm { z } ^ { 4 } } { \mathrm { y } ^ { 2 } } \right) \mathrm { j } - \frac { 4 \mathrm { z } ^ { 3 } } { \mathrm { y } } \mathbf { k }$$

• A) Not conservative
• B) Conservative

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Definitions:

Conscious Awareness

The mental state of being fully present and aware of one's thoughts, feelings, and surroundings.

Motivation

The driving force behind all actions of an organism, stemming from needs, desires, and goals.

Intrinsic Motivation

The drive to engage in an activity for its own sake, due to personal satisfaction or interest, rather than for some separable consequence.

Extrinsic Motivation

Motivation driven by external rewards, such as money, fame, grades, and praise, rather than by intrinsic enjoyment or interest in the task itself.