Chapter12Sec3ShowCode

# Chapter12Sec3ShowCode - Initialization Cells(Code Needed...

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Unformatted text preview: Initialization Cells (Code Needed for Most Plot3D Statements) In[7]:= ticks @ min_, max_ D : = Join @ Table @8 i, If @ i 0, , Style @ i, 12 DD , 8 0.01, 0 << , 8 i, Ceiling @ min D , Floor @ max D , 2 <D , H * Numbered ticks * L Table @8 j, , 8 0.01, 0 << , 8 j, Round @ min D , Round @ max- 1 D , 1 <DD H * Un- numbered ticks * L H * 2D Options * L SetOptions @ Plot, ImageSize fi 350, AxesOrigin fi 8 0, 0 < , AspectRatio fi 1, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize fi 600, BoxRatios fi 1, Boxed fi False, AxesOrigin fi 8 0, 0, 0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2, 0.9, 1 < , ViewVertical fi 8 0, 0, 1 < D ; SetOptions @ ContourPlot3D, ImageSize fi 600, BoxRatios fi 1, Boxed fi False, AxesOrigin fi 8 0, 0, 0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2, 0.9, 1 < , ViewVertical fi 8 0, 0, 1 < D ; SetOptions @ ParametricPlot3D, ImageSize fi 600, BoxRatios fi 1, Boxed fi False, AxesOrigin fi 8 0, 0, 0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2, 0.9, 1 < , ViewVertical fi 8 0, 0, 1 < D ; SetOptions @ RegionPlot3D, ImageSize fi 600, BoxRatios fi 1, Boxed fi False, AxesOrigin fi 8 0, 0, 0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2, 0.9, 1 < , ViewVertical fi 8 0, 0, 1 < D ; Chapter 12 : Vectors and the Geometry of Space 2 Chapter12Sec3.nb Section 12.3: the Dot Product ª Definition: If a = X a 1 , a 2 , a 3 \ and b = X b 1 , b 2 , b 3 \ , then the dot product (or scalar product or inner product ) of a and b is the number a b given by a b = a 1 b 1 + a 2 b 2 + a 3 b 3 . ª Example Suppose you have vectors a = X 1, 2, 3 \ and b = X- 3, 1, 2 \ , then find a b . ª Mathematica Solution In[13]:= a = 8 1, 2, 3 < b = 8- 3, 1, 2 < a.b H * This is the dot product...notice that it is a PERIOD, not a TIMES symbol ! * L a * b H * This is component multiplication * L Out[13]= 8 1, 2, 3 < Out[14]= 8- 3, 1, 2 < Out[15]= 5 Out[16]= 8- 3, 2, 6 < Properties of the Dot Product If a, b, c are vectors and c is a scalar, then 1. a a = a / 2 2. a b = b a 3. a H b + c L = a b + a c 4. H c a L b = c H a b L = a H c b L 5. a = Chapter12Sec3.nb 3 Geometric Properties If Θ is the angle between the vectors a and b , then a b = a / b / cos H Θ L ., where the angle Θ is defined to be between the two vectors, that is 0 £ Θ £ Π . Hence, we have cos H Θ L = a b a / b / . In[17]:= Show @ Plot3D @ 0, 8 x,- 0.5, 3.5 < , 8 y,- 0.5, 3.5 < , PlotRange fi 8- 3.5, 3.5 < , PlotStyle fi Directive @ Opacity @ DD , Mesh fi None, BoundaryStyle fi None D , Graphics3D @8 Thick, Blue, Arrow @88 0, 0, 0 < , 8 0, 3, 1 <<D H * The arrow command simply plots a vector...needs tail and tip points * L <D , Graphics3D @8 Thick, Red, Arrow @88 0, 1, 2 < , 8 0, 3, 1 <<D H * The arrow command simply plots a vector...needs tail and tip pointsThe arrow command simply plots a vector....
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## This note was uploaded on 01/13/2012 for the course MATH 333 taught by Professor Keithemmert during the Fall '11 term at Tarleton.

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Chapter12Sec3ShowCode - Initialization Cells(Code Needed...

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