Let P Be a Plane Through the Origin with Equation $a x - 4 y + 3 z = 0$

question 71

Essay

Let P be a plane through the origin with equation $a x - 4 y + 3 z = 0$ Let $\vec { F }$ be a vector field with curl ${ \vec {F} } = 3 \vec { i } - 5 \vec { j } + 2 \vec { k }$ Suppose $\dot {\mathbf{Q} } {\vec{F} \times \vec{d r}=0}$ for any closed curve on the plane $a x - 4 y + 3 z = 0$ Using Stokes' Theorem, determine the value of a.

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