{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 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 267 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 272 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{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 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 270 53 "Calculus Exploration 12B: Vect or Algebra and Geometry" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 269 350 "Before using this exploration you must first open \+ the Vector Routines button below and compile all the vector programs. \+ After doing this, you may then open the Vector Algebra and Geometry se ction, which provides tools for 3D vector addition, dot product, cross product, angle between two vectors, and visualization of these variou s vector operations." }{TEXT -1 0 "" }{TEXT 271 0 "" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "V ector Routines" }}{EXCHG {PARA 0 "" 0 "" {TEXT 268 72 "To compile the \+ vector routines, click in the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "restart:\nwith(linalg):\nplo t_one_vector:= proc(tail_point,tip_point)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " local tail,tip,p,xtip_text,ytip_text,ztip_text," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " xtail_text,ytail_text,ztail_text, plot_delta,dec," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " v,xv_text,yv_t ext,zv_text,j,vector_plot;\n dec:=5:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " tail:=tail_point:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " tip:=t ip_point:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " tail:=[evalf(tail[1], dec),evalf(tail[2],dec),evalf(tail[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " tip:=[evalf(tip[1],dec),evalf(tip[2],dec),evalf(tip[ 3],dec)]:" }}{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 " color=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,linest yle=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 29 " plot_delta:=.2*abs(tip[3]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " xtip_text := convert(tip[1], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ytip_text := convert(tip[2], string);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ztip_text := convert(tip[3], stri ng);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[5] := plots[textplot3d] (" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " [tip[1],tip[2],t ip[3] + plot_delta," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 " \+ ` tip point = [`||xtip_text||`,`||ytip_text||`,`||ztip_text||`]`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 " align=\{ABOVE,RIGH T\},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=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 99 " title=`vector = tip point - tail point\\n v = [`||xv_text| |`, `||yv_text||`, `||zv_text||`]`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " p[1]:=plots[spacecur ve](" }}{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=p oint,symbol=diamond):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " plot_del ta:=.2*abs(tip[3]-tail[3]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " xt ip_text := convert(tip[1], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " ytip_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 = [`|| xtip_text||`, `||ytip_text||`, `||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 := conv ert(tail[2], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " ztail_te xt := convert(tail[3], string);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[6] := plots[textplot3d](" }}{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_t ext||`, `||ztail_text||`]`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " \+ align=\{ABOVE,CENTER\},color = blue);" }}{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..6)], " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 " axes=normal,\n \+ titlefont=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 110 " title=`vector = tip point - tail point\\n v = [`||xv_text ||`, `||yv_text||`, `||zv_text||`]`\n ):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 4 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " vector_p lot" }}{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_vecto r_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 " nvecs:=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_point:=[0,0,0]:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 35 " tip_point:=op(i,list_of_vectors):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " p[2*i-1]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " [tail_point,tip_point] ," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " color=blue):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " p[2*i]:=plots[spacecurve](" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " [tip_point]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " color=blue,style=point,symbol=di amond):" }}{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 titlefont=[HELVETI CA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " t itle=`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(l ist_of_vectors::list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 " local nve cs,v1,v2,v1pv2,v3,vectors,i,tail_point,tip_point,p,dec," }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 61 " xv1,yv1,zv1,xv2,yv2,zv2,xv3,yv3,zv3,j,vector _plot:\n dec:=5:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " nvecs:=nops(li st_of_vectors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if nvecs = 2 th en" }}{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 59 " v1:=[evalf(v1[1],dec),evalf(v1[2],dec), evalf(v1[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " v2:=[evalf( v2[1],dec),evalf(v2[2],dec),evalf(v2[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " v3:=[evalf(v1pv2[1],dec),evalf(v1pv2[2],dec),evalf( v1pv2[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " vectors:=[v1,v 2,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 0 128 " \+ title=`[`||xv1||`, `||yv1||`, `||zv1||`] + [`||xv2||`, `||yv2||`, \+ `||zv2||`] =\\n [`||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_vectors)" }}{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 "pl ot_vector_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_vectors::list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " local nvecs,v 1,v2,v1dv2,vectors,i,tail_point,tip_point,p," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " part_v1,part_v2,part_v12,w1,w2,w3,dec," }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 66 " xv1,yv1,zv1,xv2,yv2,zv2,v1dv2_txt,theta,th eta_txt,j,vector_plot:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " nvecs:=n ops(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_vect ors):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " v2:=op(2,list_of_vectors ):\n dec:=5:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " v1dv2:=evalf(dot prod(v1,v2),dec):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " v1:=[evalf(v 1[1],dec),evalf(v1[2],dec),evalf(v1[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " v2:=[evalf(v2[1],dec),evalf(v2[2],dec),evalf(v2[3], dec)]:" }}{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_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 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,part_v2)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " w1:=[evalf(part_v1[1],dec),evalf(part_v 1[2],dec),evalf(part_v1[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " w2:=[evalf(part_v2[1],dec),evalf(part_v2[2],dec),evalf(part_v2[3 ],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 " w3:=[evalf(part_v12[1 ],dec),evalf(part_v12[2],dec),evalf(part_v12[3],dec)]:" }}{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 45 " degrees)/degrees,dec):" }}{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 tit lefont=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 166 " title=`[`||xv1||`, `||yv1||`, `||zv1||`] dot [`||xv2||`, `| |yv2||`, `||zv2||`] =\\n `||v1dv2_txt||`\\n theta = `||theta_txt||` de grees`,scaling=constrained):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " ve ctor_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 40 " part_v1,part_v2,part_v12,w1,w2,w3 ,dec," }}{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 39 " nvecs:=nops(list_of_vectors):\n dec:=5:" }}{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:=crossprod(v1,v2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " v1:=[evalf(v1[1],dec),evalf(v1[2],dec),evalf(v1[3], dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " v2:=[evalf(v2[1],dec),e valf(v2[2],dec),evalf(v2[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " v3:=[evalf(v1cv2[1],dec),evalf(v1cv2[2],dec),evalf(v1cv2[3],dec) ]:" }}{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 35 " \{[v3,[v3[1],v3[2],0]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " [[v3[1],0,0],[v3[1],v3[2],0]]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " [[0,v3[2],0],[v3[1],v3 [2],0]]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " color=red ,linestyle=3):" }}{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,part_v2)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " w1:=[evalf( part_v1[1],dec),evalf(part_v1[2],dec),evalf(part_v1[3],dec)]:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " w2:=[evalf(part_v2[1],dec),evalf( part_v2[2],dec),evalf(part_v2[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 " w3:=[evalf(part_v12[1],dec),evalf(part_v12[2],dec),evalf(par t_v12[3],dec)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " p[8]:=plots[sp acecurve](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " \{[w1,w 3],[w2,w3]\}," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " colo r=blue,linestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " xv1:=conv ert(v1[1], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " yv1:=conve rt(v1[2], string):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " zv1:=conver t(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(v 2[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 74 " theta:=evalf(conve rt(angle(op(1,list_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..8 )]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 " axes=normal, \n titlefont=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 186 " title=`[`||xv1||`, `||yv1||`, `||zv1||`] \+ cross [`||xv2||`, `||yv2||`, `||zv2||`] =\\n [`||xv3||`, `||yv3||`, `| |zv3||`]\\n theta = `||theta_txt||` degrees`,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_vect or_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 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot_vector_cross([[1,2,3],[-2,0,1]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Vector Algebra and Geometry" }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 0 "" }{TEXT 256 78 "1. VECTOR FROM TWO POINTS: Create a vector usi ng a tip point and a tail point." }{TEXT -1 1 "\n" }{TEXT 258 68 "Afte r entering your points, click in the red area and press [Enter]." }} {PARA 0 "" 0 "" {TEXT 272 57 "You may then click on the image and drag the view around." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "tipPoint:=[1,1,1]:\ntailPoint:=[0,0,0]:\nplot_one_vector(tailPoint,ti pPoint);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 0 "" }{TEXT 259 31 "2. VECTOR SUM: Add two v ectors." }{TEXT -1 1 "\n" }{TEXT 261 69 "After entering your vectors, \+ click in the red area and press [Enter]." }{TEXT -1 1 "\n" }{TEXT 273 57 "You may then click on the image and drag the view around." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "v:=[1,2,3]:\nw:=[-2,0,1]:\nplot_vec tor_sum([v,w]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 263 0 "" }{TEXT 262 63 "3. VECTOR DOT PRO DUCT: Compute the dot product of two vectors." }{TEXT -1 1 "\n" } {TEXT 264 69 "After entering your vectors, click in the red area and p ress [Enter]." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 274 57 "You may \+ then click on the image and drag the view around." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "v:=[1,2,3]:\nw:=[-1,0,1]:\nplot_vec tor_dot([v,w]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 266 0 "" }{TEXT 265 67 "4. VECTOR CROSS P RODUCT: Compute the cross product of two vectors." }{TEXT -1 1 "\n" } {TEXT 267 69 "After entering your vectors, click in the red area and p ress [Enter]." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 275 57 "You may \+ then click on the image and drag the view around." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "v:=[1,2,3]:\nw:=[-2,0,1]:\nplot_vec tor_cross([v,w]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "_________ ____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Filename: ExploreCalc12B.mws" }}{PARA 0 "" 0 " " {TEXT -1 36 "Copyright 2005, All Rights Reserved." }}{PARA 0 "" 0 " " {TEXT -1 44 "Permission is granted to use and modify for " }}{PARA 0 "" 0 "" {TEXT -1 37 "academic and non-commercial purposes." }}{PARA 0 "" 0 "" {TEXT -1 13 "Dr. John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "M athematics Department-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pa is@micds.org or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "UR L: http://kinetigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "______ _______________________________" }}}{MARK "12 0" 37 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }