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) \(\vec { F _ { 5 } } = 100 \left( - y ^ { 2 } x \vec { i } - z ^ { 3 } \vec { j } + z ^ { 2 } \vec { k } \right)\)

---

Definitions:

Quantitative Research

A research method focusing on obtaining data through objective measurements and statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys.

Numerical Data

Quantitative information consisting of numbers, which can be used in statistical analysis to produce findings or prove hypotheses.

Descriptive Responses

Answers or feedback that provide detailed information or elaboration on a subject.

Respondent Samples

Groups of individuals selected to participate in research or surveys, intended to represent a larger population for the purpose of gathering data.