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Questions tagged [vector-fields]

Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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Vector Calculus Problem on Gradient Cross Product

$Problem:$ If a vector function $V=V(x,y,z)$ is not irrotational, show that if there exists a scalar function $g=g(x,y,z)$ such that $gV$ is irrotational, then $$V\cdot (\nabla \times V )=0$$ ...
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The flux of a vector field

This is probably a basic question. I'm actually taking a class that introduces me to Maxwell's equations. I am currently trying to make sense of the Gauss's law and have some difficulty understanding ...
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Problem with relative reference frames [closed]

I came across this problem a while ago and I'd like to solve it, but I'm not even sure where to start. How would I start this problem and what formulas do I need? I'm not asking for a solution, but ...
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How does vectorization affect $\nabla$?

The homework and exercise was to prove $\nabla \times {A}$ transform as a vector, and I've solved it thorough hard algebra. However, something occurred to my mind and I have a hard time to resolve it....
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Why is the strain rate tensor 1/2(gradV+gradV^T)

$$\ \\1/2\left( \nabla\mathbf{u} + (\nabla\mathbf{u}) ^\mathrm{T} \right) \$$ Why is the strain rate tensor the equation above?
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