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Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices. $\mathbf{F}(x, y)=\langle\sin y, \cos x\rangle$ Figure I-VI can't copy 

   Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices.
$\mathbf{F}(x, y)=\langle\sin y, \cos x\rangle$

Figure I-VI can't copy
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 16, Problem 17 ↓
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Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices. $\mathbf{F}(x, y)=\langle\sin y, \cos x\rangle$ Figure I-VI can't copy
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Match the vector fields $F$ with the plots labeled I-IV. Give reasons for your choices. $$ \mathbf{F}(x, y)=\langle y, y+2\rangle $$
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Transcript

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00:01 So we'd like to match the vector fields with the plots labeled here.
00:05 We have the sine y, cosine x.
00:08 So that means we expect whenever y is equal to 0, we have sine y equals 0.
00:16 So along the x -axis, all of the direction should be going in.
00:24 The x should be 0, and everything should be vertical at the x -axis.
00:29 So it's definitely not this one.
00:32 And we're different just on that thing.
00:37 Okay, great.
00:38 Also, when x equals 0, we have cosine x equals 1.
00:43 So it should be going up along the entire y -axis.
00:49 It's not that.
00:50 This looks like it's horizontal on the y -axis...
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