How do I draw a vector field by hand? F(x,y,z)=-y k

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How do I draw a vector field by hand? F(x,y,z)=-y k

Mathematics
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\(\vec{F}(x,y,z)=-y\cdot\vec{k}\)
Yes

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I'm not sure what you did there?
I'm not sure what she did there either.
This field doesn't depent on \(x\) and \(z\). That means that there will be the same vectors in the planes \(y=\text{const}\). \(\vec{k}\) is a vector that has length = 1 and is collinear to \(z\)-axis. I drew 3 planes \(y=\text{const}\) for different values of this constant.
So, say (1,0,0).. it would be the zero vector, so wouldn't it just be a point and not a line of length 1?
A vector field is a vector function. Its argument is a vector (point) and its value is also a vector. For example if you take a point (1,0,0), thats mean that \(x=1,y=z=0.\). So, \(\vec{F}(1,0,0)=0\cdot\vec{k}=\vec{0}\). For every vector that has y-coordinate = 0, it will be zero vector. y=0 is a plane. Every vector in this plane will be zero-vector. If you take (0,1,0), then \(\vec{F}(0,1,0)=1\cdot\vec{k}=\vec{k}\). Every vector in the plane y=1 will be \(\vec{k}\). And so on.
I get it!! Thank you so much! So everything with a negative y value would be going up and everything with a positive y value would be going down?
Yes. Sorry, my fault. I have lost the "-" sign. I'm happy that you've got it. You are welcome.
Thank you!

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