RowBox[{StyleBox[RowBox[{Exercise,  , 2.1, .3,  , (modified)}], Subsubtitle], :, , Cel ... Size -> {524., 279.}, ImageMargins -> {{0., 0.}, {0., 0.}}, ImageRegion -> {{0., 1.}, {0., 1.}}]}]

<<Graphics`Graphics` <<Graphics`PlotField` <<Graphics`ImplicitPlot`

(a)

w1 = ImplicitPlot[Table[x * y == u, {u, -4, 4, 1}], {x, -3, 3}, {y, -3, 3}]

[Graphics:HTMLFiles/Ex2.1.3_4.gif]

⁃Graphics⁃

w2 = ImplicitPlot[Table[x^2 - y^2v, {v, -4, 4, 1}], {x, -3, 3}, {y, -3, 3}]

[Graphics:HTMLFiles/Ex2.1.3_7.gif]

⁃Graphics⁃

(b)

Show[w1, w2]

[Graphics:HTMLFiles/Ex2.1.3_10.gif]

⁃Graphics⁃

Intersections are clearly at right angles.

(c)

RowBox[{w3, =, RowBox[{PlotGradientField, [, RowBox[{x y, ,, {x, -3, 3}, ,, {y, -3, 3}, ,, Row ... [{ScaleFunction, ,  , RowBox[{(, RowBox[{1., &}], )}]}]}], ]}]}] Show[w1, w2, w3, w4]

[Graphics:HTMLFiles/Ex2.1.3_13.gif]

⁃Graphics⁃

The unit vectors are clearly orthogonal.  The scale option is needed to plot unit vectors rather than just the gradient.


Created by Mathematica  (September 29, 2003)