Match the vector field with its graph. F(x,y) = yi? I tried drawing my own graph and got something other than the answer choices

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1 Answer
Jul 28, 2018

#bbF(x,y) = ybbi#

Immediately, you can tell that vector #bbF# only ever points in the #bbi# direction, ie along the x-axis

That eliminates everything but the bottom left-hand option

Plus, mathematically, the #x# variable is irrelevant

So, from there, maybe just plug in some values:

  • #bbF(x,1) = bbi qquad bbF(x,2) = 2bbi#

  • #bbF(x,-1) = - bbi qquad bbF(x,-2) = - 2bbi#

That bottom left-hand option looks even more interesting.

In terms of yer confusion , don't count the number of arrows, compare the length of arrows. Arrow length is increasing linearly