Suppose that $\hat { Q } _ { ∘ } \vec { G } \times d \vec { r } = 5 a ^ { 3 } + 4 a ^ { 2 }$ where C_a is the circle $\vec { r } ( t ) = ( a \cos t + 5 ) \vec { i } - ( a \sin t + 4 ) \vec { j } + 20 \vec { k }$ for any a > 0.
Does knowing this tell you anything about curl $\vec { G } ( 5,4,20 ) ?$ Is so, what? If not, why not?

Question

Suppose that

\hat { Q } _ { ∘ } \vec { G } \times d \vec { r } = 5 a ^ { 3 } + 4 a ^ { 2 }

where C_a is the circle

\vec { r } ( t ) = ( a \cos t + 5 ) \vec { i } - ( a \sin t + 4 ) \vec { j } + 20 \vec { k }

for any a > 0.
Does knowing this tell you anything about curl

\vec { G } ( 5,4,20 ) ?

Is so, what? If not, why not?

Quizplus · Accepted Answer

The Answer of Suppose that $\hat { Q } _ { ∘ } \vec { G } \times d \vec { r } = 5 a ^ { 3 } + 4 a ^ { 2 }$ where C_a is the circle $\vec { r } ( t ) = ( a \cos t + 5 ) \vec { i } - ( a \sin t + 4 ) \vec { j } + 20 \vec { k }$ for any a > 0. Does knowing this tell you anything about curl $\vec { G } ( 5,4,20 ) ?$ Is so, what? If not, why not?

Suppose That Q^∘G⃗×dr⃗=5a3+4a2\hat { Q } _ { ∘ } \vec { G } \times d \vec { r } = 5 a ^ { 3 } + 4 a ^ { 2 }Q^​∘​G×dr=5a3+4a2

Suppose That $\hat { Q } _ { ∘ } \vec { G } \times d \vec { r } = 5 a ^ { 3 } + 4 a ^ { 2 }$