Question

F(x,y,z)=xi+yj+zk
Match the vector fields F with the plots.
I picked IV because x y and z were all 1 unit, but if it wasn't for the process of elimination, I wouldn't have been able to figure it out. Please help

Answer 1

I figured since IV is the only figure where x=1 y=1 and z=1, it must be the right match.

Answer 2

Looks like it would be II. They would be branching out in all directions because they all have the same coefficient, 1

Answer 3

it seems like the length of the arrows are changing in II

Answer 4

That's just the way it's viewed. IV can't be correct because the arrows are pointed in a single direction, but all the coefficients are the same, so that can't happen.

Answer 5

Try this: http://www.slu.edu/classes/maymk/banchoff/VectorField.html you can view and navigate through each vector field

Answer 6

so is the origin in the center of the box...I don't seem to be able to connect the box to this

Answer 7

to make a connection in my head I mean

Answer 8

yep and since they all have a coefficient of one, they will branch out in the x,y, and z direction evenly

Answer 9

In what way...