{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 18 "" 0 "" {TEXT -1 11 "\277\271\301\246 1.3.16" }} {PARA 19 "" 0 "" {TEXT -1 8 "\261\350 \277\353 \261\270" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "\276\306\267\241\300 \307 \271\346\271\375\300\272 \261\263\260\372\274\255\300\307 \263 \273\277\353\300\273 \265\373\270\245\260\315\300\314\264\331." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(geom3d):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "L[1]:=spacecurve([t,(1/2)*t,(t-6)/3], t=-12..12, color=blue, t hickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "P:=plot3d([ x,y,(2*x+y-5)/2],x=-12..12,y=-7..7):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "display(L[1],P);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "point(o,t,1/2*t,-2+t/3):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 30 "plane(p, 2*x+y-2*z=5,[x,y,z]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d:=distance(o,p):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ans:=[solve(d=7,t)]:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "for i to nops(ans) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "ans:= subsop(i=subs(t=op(i,ans), coordinates(o)),ans) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 4 "ans;" }}}{PARA 0 "" 0 "" {TEXT -1 213 "\277\251\261 \342\277\241\274\255\264\302 \301\367\274\261 \300\247\300\307 \307 \321\301\241 X(t)\270\246 \301\366\263\252\260\355 \271\346\307\342 \300\314 \301\326\276\356\301\370 \306\362\270\351\300\307 \271\375 \274\261\300\316 \301\367\274\261\300\307 \275\304\300\273 \261\270 \307\321 \265\332\277\241 \300\314 \301\367\274\261\300\314 \260\356 \270\351\260\372 \270\270\263\252\264\302 \301\241 P\270\246 \261\270 \307\321 \265\332 \300\314 \301\241 P\267\316\272\316\305\315 \301\367 \274\261 \273\363\300\307 \301\241 X(t)\261\356\301\366\300\307 \260 \305\270\256\260\241 7\300\316\265\307\264\302 \301\367\274\261 \273 \363\300\307 \301\241\300\273 \261\270\307\317\264\302 \271\346\271 \375\300\314\264\331." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest art;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "N:=vector(3,[2,1,-2]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "T:=vector(3,[t,(1/2)*t,1/3*t -2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "L:=evalm(T+s*N);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "E:=2*L[1]+L[2]-2*L[3]-5=0 ;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sol:=so lve(E,s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "P:=vector(3, [ evalm(subs(s=sol, L[1])),evalm(subs(s=sol, L[2])),evalm(subs(s=sol, L[ 3]))]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dotprod(N,P);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "assume( t>0 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dotprod(T-P,T-P);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Q:=solve(%=49,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "ans[1]:=vector(3,[subs(t=Q[1],T[1]),subs( t=Q[1],T[2]),subs(t=Q[1],T[3])]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "ans[2]:=vector(3,[subs(t=Q[2],T[1]),subs(t=Q[2],T[2]) ,subs(t=Q[2],T[3])]);" }}}{PARA 0 "" 0 "" {TEXT -1 114 "\277\251\261 \342\277\241\274\255\264\302 \301\367\274\261 \300\247\300\307 \307 \321\301\241\277\241\274\255 \301\326\276\356\301\370 \306\362\270\351 \261\356\301\366\300\307 \260\305\270\256\270\246 \261\270\307\317\264 \302 \275\304\300\273 \300\314\277\353\307\317\277\251 \260\305\270 \256\260\241 7\300\314\265\307\264\302 \301\367\274\261\300\247\300 \307 \301\241\300\273 \261\270\307\317\277\264\264\331." }{TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "P:=vector(3,[1,1,-1]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 33 "Q:=vector(3,[t,(1/2)*t,1/3*t-2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "N:=vector(3,[2,1,-2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "d:=abs(dotprod(N,(P-Q)))/norm(N,2); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(d=7,t);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "ans[1]:=vector(3, [subs(t=12,Q[1]),subs(t=12,Q[2]),subs(t=12,Q[3])]);" }{TEXT -1 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "ans[1]:=vector(3,[subs(t=-1 20/11,Q[1]),subs(t=-120/11,Q[2]),subs(t=-120/11,Q[3])]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }