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I have looked at the graph. As far as I know, radial is when all of the vectors are pointing away from the orgin, which they are. How can I prove if a function is radial (not just look at a graph). I would like a formula, not an example. Even if my function is not radial, I would still like to know computations to prove if a vector field is radial or not.

My function F(x-y, y+x) For a graphing site:

Function: (x-y)i+(x+y)j

Thank you!

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A field $\vec F(\vec r)$ is radial if for every position vector $\vec r$ the vectors $\vec F(\vec r)$ and $\vec r$ are collinear. That is, one is a scalar multiple of the other.

The cross-product helps to determine collinearity in 2 and 3 dimensions. In two dimensions, this is simply a 2x2 determinant made of both vectors.

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