Question

Vector field, how do I sketch F(x,y,z) = -yk

Answer 1

So it's F(0,0,1) = -k

Answer 2

<0,0,-1>

Answer 3

You have the correct sketch for the vector field F(0,0,1) = -k. Basically everything points down and every vector is of length 1.

To sketch F(x,y,z) = -yk, you basically keep everything the same but the vectors will change in length depending on what y is. So for example, if y = 0, then you have 0 vectors. This is going to happen within the xz plane where y = 0. Now let's say y = 2. Now you have the vector -2k = <0,0,-2>. If y = 3, then you now have -3k = <0,0,-3> etc.

Answer 4

Hey, sorry for the late reply, so then there would also be upward arrows, and they will be vary in sizes because of the unit vector?

Answer 5

so like this kind off