Wood Flynn
07/13/2024 · Primary School
Given the vector fileld \( \vec{u}\left(u_{x}, u_{y}, u_{z}\right)=\left(3 x^{2} y, y z, 3 x z^{2}\right) \), calculate the Iaplacion of \( \vec{u}, \vec{\nabla}^{2} \vec{u} \) that is : \( \vec{\nabla}^{2} \vec{u}=\left(\vec{\nabla}^{2} u_{z}\right) \vec{i}+\left(\vec{\nabla}^{2} u_{y}\right) \vec{j}+\left(\vec{\nabla}^{2} u_{z}\right) \vec{k} \)
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The Laplacian of the vector field \(\vec{u}\) is \(\nabla^2 \vec{u} = 6y \vec{i} + 0 \vec{j} + 6x \vec{k}\).
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