{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text \+ Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 3 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Vector Routines" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "wi th(linalg):\nplot_one_vector:= proc(tail_point,tip_point)" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 48 " local tail,tip,p,xtip_text,ytip_text,ztip_t ext," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " xtail_text,ytail_text,zta il_text,plot_delta," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " v,xv_text, yv_text,zv_text,j,vector_plot;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " \+ tail:=tail_point:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " tip:=tip_poin t:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 " tail:=[evalf(tail[1],2),eval f(tail[2],2),evalf(tail[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 " tip:=[evalf(tip[1],2),evalf(tip[2],2),evalf(tip[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " if iszero(tail) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " p[1]:=plots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " \{[[tip[1],0,0],[tip[1],tip[2],0]]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " [[0,tip[2],0],[tip[1] ,tip[2],0]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " col or=magenta,linestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " p[2]:= plots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ \{[tip,[tip[1],tip[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " \+ [[0,0,0],[tip[1],tip[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [tip,[0,0,tip[3]]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " color=red,linestyle=3):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 " p[3]:=plots[spacecurve](" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 19 " [tail,tip]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " p[ 4]:=plots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " [ tip]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " color=blue,style=p oint,symbol=diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " plot_del ta:=.2*abs(tip[3]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " xtip_text \+ := convert(tip[1], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " yt ip_text := convert(tip[2], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ztip_text := convert(tip[3], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[5] := plots[textplot3d](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " [tip[1],tip[2],tip[3] + plot_delta," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 " ` tip point = [`||xti p_text||`,`||ytip_text||`,`||ztip_text||`]`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 " align=\{ABOVE,RIGHT\},color = blue);\n #v:=add(tip,scalarmul(tail,-1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " v:=matadd(tip,scalarmul(tail,-1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " xv_text:=convert(v[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " yv_text:=convert(v[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " zv_text:=convert(v[3], string):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 29 " vector_plot:=plots[display](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [seq(p[j],j=1..5)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 " axes=normal,\n titlefont=[HELV ETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 " title=` vector = tip point - tail point = [`||xv_text||`, `||yv_text||`, `||zv _text||`]`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " else" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 " p[1]:=plots[spacecurve](" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 41 " \{[tail,[tail[1],tail[2],0]]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " [[tail[1],0,0],[tail[ 1],tail[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " [[ 0,tail[2],0],[tail[1],tail[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " [tail,[0,0,tail[3]]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " color=red,linestyle=3):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 " p[2]:=plots[spacecurve](" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 38 " \{[tip,[tip[1],tip[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " [[tip[1],0,0],[tip[1],tip[2], 0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " [[0,tip[2],0] ,[tip[1],tip[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " \+ [tip,[0,0,tip[3]]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " \+ color=red,linestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " \+ p[3]:=plots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " \+ [tail,tip]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " color=blue) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " p[4]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " [tip]," }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 47 " color=blue,style=point,symbol=diamond):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " plot_delta:=.2*abs(tip[3]-tail[3] ):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " xtip_text := convert(tip[1] , string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ytip_text := conver t(tip[2], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ztip_text : = convert(tip[3], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[5 ] := plots[textplot3d](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " \+ [tip[1],tip[2],tip[3] + plot_delta," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 " ` tip point = [`||xtip_text||`, `||ytip_t ext||`, `||ztip_text||`]`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " \+ align=\{ABOVE,CENTER\},color = blue);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " xtail_text := convert(tail[1], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " ytail_text := convert(tail[2], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " ztail_text := convert(tail[3], \+ string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[6] := plots[textplo t3d](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " [tail[1],tail[2 ],tail[3] + plot_delta," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 " \+ ` tail point = [`||xtail_text||`, `||ytail_text||`, `||ztail_text||`] `]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " align=\{ABOVE ,CENTER\},color = blue);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " v:=ma tadd(tip,scalarmul(tail,-1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " \+ xv_text:=convert(v[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " yv_text:=convert(v[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " zv_text:=convert(v[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " vector_plot:=plots[display](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [seq(p[j],j=1..6)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 " axes=normal,\n titlefont=[HELVETICA,DEFAUL T,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 " title=`vector = tip point - tail point = [`||xv_text||`, `||yv_text||`, `||zv_text||`]`): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " vector_plot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot_one_vector([0,0,0],[1,1,1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 46 "plot_vector_list:= proc(list_of_vectors::list)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " local nvecs,i,tail_point,tip_point ,p,n,nv_text,j,vector_plot:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " nve cs:=nops(list_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " for \+ i from 1 to nvecs do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " tail_poin t:=[0,0,0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " tip_point:=op(i,li st_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " p[2*i-1]:=plot s[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " [tai l_point,tip_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " \+ color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[2*i]:=plots[sp acecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " [tip_point ]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " color=blue,style=p oint,symbol=diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " n:=2*nvecs:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " nv_text:=convert(nvecs, string):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 29 " vector_plot:=plots[display](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [seq(p[j],j=1..n)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 76 " axes=normal,\n titlef ont=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " \+ title=`Plot a list of `||nv_text||` vectors||`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " vector_plot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot_ vector_sum:= proc(list_of_vectors::list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " local nvecs,v1,v2,v1pv2,v3,vectors,i,tail_point,tip_ point,p," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " xv1,yv1,zv1,xv2,yv2,z v2,xv3,yv3,zv3,j,vector_plot:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " n vecs:=nops(list_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if nvecs = 2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v1:=op(1,list_ of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v2:=op(2,list_of_ vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " v1pv2:=matadd(v1,v2) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v1:=[evalf(v1[1],2),evalf(v1 [2],2),evalf(v1[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v2:=[e valf(v2[1],2),evalf(v2[2],2),evalf(v2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " v3:=[evalf(v1pv2[1],2),evalf(v1pv2[2],2),evalf(v1pv 2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " vectors:=[v1,v2,v3]: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " for i from 1 to 3 do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " tail_point:=[0,0,0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " tip_point:=op(i,vectors):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 31 " p[2*i-1]:=plots[spacecurve](" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 " [tail_point,tip_point]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " color=blue):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " p[2*i]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " [tip_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " color=blue,style=point,symbol =diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " p[7]:=plots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " \{[v1,v3]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " [v2,v3]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " color=blue,linestyle=3):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 " p[8]:=plots[spacecurve](" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 35 " \{[v3,[v3[1],v3[2],0]]," }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 44 " [[v3[1],0,0],[v3[1],v3[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " [[0,v3[2],0],[v3[1] ,v3[2],0]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " colo r=red,linestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 " p[9]:=plot s[textplot3d]([v3[1],v3[2],max(v1[3],v2[3],v3[3])+.5," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 " `Parallelogram Law for Vector Addition`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ color=blue," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " \+ align=\{ABOVE,CENTER\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv1:=convert(v1[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv1:=convert(v1[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv1:=convert(v1[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv2:=convert(v2[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv2:=convert(v2[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv2:=convert(v2[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv3:=convert(v3[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv3:=convert(v3[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv3:=convert(v3[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " vector_plot:=plots[display](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [seq(p[j],j=1..9)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 " axes=normal,\n titlefont= [HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 126 " \+ title=`[`||xv1||`, `||yv1||`, `||zv1||`] + [`||xv2||`, `||yv2||`, \+ `||zv2||`] = [`||xv3||`, `||yv3||`, `||zv3||`]`):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 12 " vector_plot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " \+ else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " plot_vector_list(list_of_v ectors)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " fi:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 4 "end:" }}{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot_v ector_sum([[1,2,3],[-2,0,1]]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot_vector_dot:= proc(list_of_ve ctors::list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " local nvecs,v1,v2, v1dv2,vectors,i,tail_point,tip_point,p," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " part_v1,part_v2,part_v12,w1,w2,w3," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " xv1,yv1,zv1,xv2,yv2,zv2,v1dv2_txt,theta,theta_txt,j ,vector_plot:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " nvecs:=nops(list_ of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if nvecs = 2 then " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v1:=op(1,list_of_vectors):" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v2:=op(2,list_of_vectors):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " v1dv2:=evalf(dotprod(v1,v2),2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v1:=[evalf(v1[1],2),evalf(v1[2] ,2),evalf(v1[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v2:=[eval f(v2[1],2),evalf(v2[2],2),evalf(v2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " vectors:=[v1,v2]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " for i from 1 to 2 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " \+ tail_point:=[0,0,0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " tip_poin t:=op(i,vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " p[2*i-1]:=p lots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " \+ [tail_point,tip_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " \+ color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " p[2*i]:=pl ots[spacecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " [ti p_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " color=blue ,style=point,symbol=diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " o d:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " part_v1:=matadd(.3*v1,0):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " part_v2:=matadd(.3*v2,0):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " part_v12:=evalf(matadd(part_v1,pa rt_v2)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " w1:=[evalf(part_v1[1] ,2),evalf(part_v1[2],2),evalf(part_v1[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " w2:=[evalf(part_v2[1],2),evalf(part_v2[2],2),evalf( part_v2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 " w3:=[evalf(par t_v12[1],2),evalf(part_v12[2],2),evalf(part_v12[3],2)]:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 " p[5]:=plots[spacecurve](" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 32 " \{[w1,w3],[w2,w3]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " color=red,linestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv1:=convert(v1[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv1:=convert(v1[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv1:=convert(v1[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv2:=convert(v2[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv2:=convert(v2[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv2:=convert(v2[3], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " v1dv2_txt:=convert(v1dv2, string):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " theta:=evalf(convert(angle(op(1,l ist_of_vectors),op(2,list_of_vectors))," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " degrees)/degrees,4):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " theta_txt:=convert(theta,string):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 " vector_plot:=plots[display](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " [seq(p[j],j=1..5)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 " axes=normal,\n title font=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 166 " \+ title=`[`||xv1||`, `||yv1||`, `||zv1||`] dot [`||xv2||`, `||y v2||`, `||zv2||`] = `||v1dv2_txt||` and theta = `||theta_txt||` degree s`,scaling=constrained):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " vector _plot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " plot_vector_list(list_of_vectors)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot_vector_dot([[1,2,3],[-1,0,1]]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot_vector_cro ss:= proc(list_of_vectors::list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " local nvecs,v1,v2,v1cv2,v3,vectors,i,tail_point,tip_point,p," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " part_v1,part_v2,part_v12,w1,w2,w3 ," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " xv1,yv1,zv1,xv2,yv2,zv2,xv3, yv3,zv3,theta,theta_txt,j,vector_plot:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " nvecs:=nops(list_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if nvecs = 2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v1: =op(1,list_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " v2:=op (2,list_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " v1cv2:=cr ossprod(v1,v2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v1:=[evalf(v1[ 1],2),evalf(v1[2],2),evalf(v1[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " v2:=[evalf(v2[1],2),evalf(v2[2],2),evalf(v2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " v3:=[evalf(v1cv2[1],2),evalf(v1cv2[2],2 ),evalf(v1cv2[3],2)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " vectors: =[v1,v2,v3]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " for i from 1 to 3 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " tail_point:=[0,0,0]:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " tip_point:=op(i,vectors):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " p[2*i-1]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " [tail_point,tip_point ]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " color=blue):" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " p[2*i]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " [tip_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " color=blue,style=point,symbol =diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " p[7]:=plots[spacecurve](" }}{PARA 0 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