[PDF] [PDF] Lesson 17: Vector Fields (161) - Purdue Math





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Match the following vector fields (A-D) with their plots (I-IV). A. F(x y) = <3



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[PDF] Lesson 17: Vector Fields (161) - Purdue Math

Match the following vector fields (A-D) with their plots (I-IV) A F(x y) = (Vector fields made in the Geogebra 3d vector field plotter)



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[PDF] Lesson 17: Vector Fields (161) - Purdue Math

MA 261, Lesson 17

Ex 2. Match the following vector elds (A-D) with their plots (I-IV).

A:~F(x;y) =h3;xiB:~F(x;y) =hy;yiC:~F(x;y) =hx;2iD:~F(x;y) =hlnx2;yi(Vector elds made in the Kevin Mehall vector eld plotter)

(Answer on next page) 1

MA 261, Lesson 17

For A, notice that they-component only depends on the vector'sx-position. Hence, all vertical lines should have the same vector along them. Notice also that ifxis positive, then the vectors point up and to the right. Ifxis negative, vectors point down and to the right.

This happens with vector eld IV.

For B, notice that both thex- andy-components only depend on the vector'sy-position, so all horizontal lines should have the same vector along them. Notice also that ifyis positive, the vectors should point up and to the right. Ifyis negative, the vectors should point down and to the left. This happens with vector eld I. For C, notice that thex-component depends only on thex-position, and they-component is constant. Whenxis positive, vectors point right and up. Whenxis negative, vectors point left and up. This happens with vector eld II. For D, notice that thex-component is undened whenx= 0 and that the vectors should be identical on opposite sides of they-axis. This happens with vector eld III. 2

MA 261, Lesson 17

Ex 3. Match the following vector elds (A-D) with their plots (I-IV).

A:~F(x;y;z) =hy;x;0iB:~F(x;y;z) =hz;y;xi

C:~F(x;y;z) =hcosz;1;1iD:~F(x;y;z) =hx;y2;1i(Vector elds made in the Geogebra 3d vector eld plotter) (Answer on next page) 3

MA 261, Lesson 17

For A, notice that thez-component is 0. Hence, all vectors are horizontal. This happens in vector eld II. For C, notice that theyandzvalues are both constant, and thex-value depends on the cosine of thez-value. Hence thex-value should oscillate, and lines perpendicular to the yz-plane should all have the same vector. This happens in vector eld III. For D, notice that they- andz-components are always nonnegative, so all the vectors should be pointing in the positivey-direction and positivex-direction. This happens with vector eld I. By process of elimination, B must be IV. Notice also that the direction the vector is pointing depends on which octant the vector is, and the vectors get larger as you move away from the origin, which is exhibited in IV. 4quotesdbs_dbs7.pdfusesText_5
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