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

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