Solve the Problem $\mathrm { G } = \mathrm { P } ( \mathrm { x } , \mathrm { y } ) \mathbf { i } + \mathrm { Q } ( \mathrm { x } , \mathrm { y } ) \mathbf { j }$

question 166

Multiple Choice

Solve the problem.
-Find a field $\mathrm { G } = \mathrm { P } ( \mathrm { x } , \mathrm { y } ) \mathbf { i } + \mathrm { Q } ( \mathrm { x } , \mathrm { y } ) \mathbf { j }$ in the $x y - p l a n e$ with the property that at any point $( a , b ) \neq ( 0,0 ) , \mathrm { G }$ is a unit vector pointing away from the origin.

• A) \(- \frac { x i + y j } { \sqrt { x ^ { 2 } + y ^ { 2 } } }\)
• B) \(x i + y j\)
• C) \(\frac { x i + y j } { \sqrt { x ^ { 2 } + y ^ { 2 } } }\)
• D) \(\frac { x i - y j } { \sqrt { x ^ { 2 } - y ^ { 2 } } }\)

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Definitions:

Economic Subsystem

A division within a larger economic system that operates its own particular processes or functions, such as agriculture or manufacturing.

Adaptive

Characterizing an ability or tendency to adjust effectively to new conditions or environments.

Imperative

Describes something that is absolutely necessary or required, often used in the context of commands or duties.

Integration Imperative

The perceived need or policy goal of integrating diverse groups into a cohesive and functioning society, emphasizing unity and cooperation.