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Consider the following continuously differentiable function $$\textbf{v}(x,y,z)=3x^2y \textbf{ i} + 8y^2z \textbf{ j} + 5xyz \textbf{ k}$$ where $\textbf{i, j,}$ and $\textbf{k}$ represent the respective unit vectors along the $x,y,$ and $z$ directions in the Cartesian coordinate system. The curl of this function is

  1. $-3x^2 \textbf{ i}-8y^2 \textbf{ j} +5z(x+y) \textbf{ k}$
  2. $6xy \textbf{ i}-16 yz \textbf{ j} +5xy \textbf{ k}$
  3. $(5xz-8y^2) \textbf{ i}-5yz \textbf{ j} -3x^2 \textbf{ k}$
  4. $y(11x+16z)$
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