For the following integral, say whether Stokes' Theorem, the Divergence Theorem, or neither applies. $\dot{\mathrm { Q }} \left( 6 y \vec { i } + 9 z ^ { 2 } \vec { j } + 2 \vec { k } \right) \times \vec { d r }$ where C is a closed loop in space.
A)Stokes' Theorem
B)Divergence Theorem.
C)Neither

Question

Quizplus · Accepted Answer

Stokes' Theorem applies because the integral is a line integral over a closed loop in space, which is exactly the scenario where Stokes' Theorem is used to relate a line integral to a surface integral.

For the Following Integral, Say Whether Stokes' Theorem, the Divergence Q˙(6yi⃗+9z2j⃗+2k⃗)×dr⃗\dot{\mathrm { Q }} \left( 6 y \vec { i } + 9 z ^ { 2 } \vec { j } + 2 \vec { k } \right) \times \vec { d r }Q˙​(6yi+9z2j​+2k)×dr

For the Following Integral, Say Whether Stokes' Theorem, the Divergence $\dot{\mathrm { Q }} \left( 6 y \vec { i } + 9 z ^ { 2 } \vec { j } + 2 \vec { k } \right) \times \vec { d r }$