(Solved): If \( \mathbf{F}(x, y, z)=\langle 0,1,0\rangle \), which of the follov P. The flux of \( \mathrm{F} ...

If \( \mathbf{F}(x, y, z)=\langle 0,1,0\rangle \), which of the follov P. The flux of \( \mathrm{F} \) across the xy-plane is zero. Q. The flux of \( \mathrm{F} \) across the \( \mathrm{yz} \)-plane is zero. R. The flux of \( \mathbf{F} \) across the \( x z \)-plane is zero. Q only P only R only \( Q \) and \( R \) \( P \) and \( Q \) Let \( \mathrm{C} \) be a smooth curve in \( \mathbb{R}^{3} \), let \( \mathrm{S} \) be a smooth surface in \( \mathbb{R}^{3} \). Assume that \( \mathrm{f}(\mathrm{x}, \mathrm{y}, \mathrm{z}) \) is a scalarvalued function with continuous first partial derivatives and \( F(x, y, z) \) is a vector-valued function with continuous first partial derivatives for each component. Identify the following integrals. \( \int_{C} \operatorname{div} \mathbf{F} d r \) is a \( \iint_{S} \nabla f \cdot d \mathbf{S} \) is a