Which of the Following Vector Fields Has the Following Properties $\frac { 3 } { 5 } \vec { i } + \frac { 4 } { 5 } \vec { j }$

question 6

Multiple Choice

Which of the following vector fields has the following properties: 1) the largest value of its circulation density at (1,2,1) is 50
2) the largest value of its circulation density at (1,2,1) occurs around the direction $\frac { 3 } { 5 } \vec { i } + \frac { 4 } { 5 } \vec { j }$

• A) \(\vec { F } _ { 1 } = - y ^ { 2 } x \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k }\)
• B) \(\vec { F _ { 2 } } = \frac { 1 } { 100 } \left( - y ^ { 2 } \times \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k } \right)\)
• C) \( { \vec { F } _ { 3 } } = \frac { 1 } { 10 } \left( - y ^ { 2 } x \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k } \right)\)
• D) \( { \vec { F } _ { 4 } } = 10 \left( - y ^ { 2 } x \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k } \right)\)
• E) \(\vec { F _ { 5 } } = 100 \left( - y ^ { 2 } x \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k } \right)\)

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Definitions:

Earnings Per Share

A company's profit divided by the outstanding shares of its common stock, indicating profitability.

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The ongoing market price for an asset or service available for purchase or sale.

Total Asset Turnover

A financial ratio that measures the efficiency of a company's use of its assets to generate sales revenue.

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A measure calculated by averaging the total assets a company has at the beginning and end of the financial period, used to evaluate asset efficiency.