# 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

Jul 28, 2018

$\boldsymbol{F} \left(x , y\right) = y \boldsymbol{i}$

Immediately, you can tell that vector $\boldsymbol{F}$ only ever points in the $\boldsymbol{i}$ 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:

• $\boldsymbol{F} \left(x , 1\right) = \boldsymbol{i} q \quad \boldsymbol{F} \left(x , 2\right) = 2 \boldsymbol{i}$

• $\boldsymbol{F} \left(x , - 1\right) = - \boldsymbol{i} q \quad \boldsymbol{F} \left(x , - 2\right) = - 2 \boldsymbol{i}$

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