ZXTape! 0Created with Ramsoft MakeTZXVECTORS \\k^X0:7:0::"PART 2":0:7:18,0;:"PART 3" DPART 2 @2z<~B<|~<|BB<<~B<|~|><@B|<|>B<@@<<<<$@B@BBBf@B@BBB@BDB@BBBbB@@B(BBBB $B@@BDBB??????BB@ZBD@BB@?????????DBBFB@@BBB???????????????~B<@~<B<~BB<|>BB~~<><<<<@@@@><@@@@B@@@@@@@@@@@@@@???????????????B@@?????@?????@?????><~@@@@@@GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBV@GGGGGGGGGGGGGGGGGGGGGGGGGGGGBVt@GGGGGGGGGGGGGGGGGGGGGGGGGGGBVte@GGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGPART 3 6 4"6 7200  (op=(i*i+j*j+k*k) ,ii=0502 0i=0j=060< 2 a=(i/op) 3 b=(j/op) 4 c=(k/op) < v=v+1 > 7600 @p$""70F BV20,0;"Press D if you want a diagram; otherwise press any other letter" D,7500L:a$=i$:20,0;z$;z$ Ea$"D"p$="" FDoo+i<1oo+i>254pp+j<16pp+j>15980P Gi=0j=075K Hp$=""a$="D"150 Ko=oo+i:p=pp+j N 7650 Poo=oo+i:pp=pp+j Rii=ii+i:jj=jj+j:kk=kk+k Topp=(ii*ii+jj*jj+kk*kk) Vopp=0100d Z&ii/opp=1aa=0:94^ \aa=(ii/opp) ^&jj/opp=1bb=0:98b `bb=(jj/opp) b&k/opp=1cc=0:100d ccc=(kk/opp) d20,0;"Press: V-values ";("R-repeat mode; any other letter - new mode" ch=2);(" any other letter - continue"ch=7) e vlt=vlt+op f7500L:a$=i$ ha$="V"120x jch=7 la$"R"240 n 1100L xl$=(v-1) zv=65Al$="O" |6ch=2ex=1:1:1101M:0 }128:146 1 2;3,0;" ";l$;v;"=";(op*100d+.5)/100d;1;" i:";(i*100d+.5)/100d'" j:";(j*100d+.5)/100d;" k:";(k*100d+.5)/100d '" Angles: A=";(r*a*100d+.5)/100d'" B=";(r*b*100d+.5)/100d;" C=";(r*c*100d+.5)/100d '" COS: L=";(a*100d+.5)/100d;" M=";(b*100d+.5)/100d'" N=";(c*100d+.5)/100d 2''" O";v;"=";(100d*((ii*ii+jj*jj+kk*kk))+.5)/100d;1;" it=";(ii*100d+.5)/100d;" jt=";(jj*100d+.5)/100d'" kt=";(kk*100d+.5)/100d;" lt=";(vlt*100d+.5)/100d opp=0144 aa=0145 '" Angles AT=";(r*aa*100d+.5)/100d'" BT=";(r*bb*100d+.5)/100d;" CT=";(r*cc*100d+.5)/100d 0: Ech=7quit=1:7400:1:128:0: U20,0;"Press: R-repeat mode; any other letter - new mode " =7500L:i$="R"1:128:0:1100L 240 q=0 w=pp+jpp-1*j ?oo+i>255oo+i<1w>159w<16158 oo,w oo+i,w w w=oo+ioo-1*i ?w>255w<1pp+j>159pp+j<16168 w,pp w,pp+j w 75K Fz=0:quit=z:r=57.296e/:oo=127:pp=87W:a$="C" 0ii=z:jj=z:kk=z:vlt=z:opp=z:o=z:p=z:aa=z %v=64@:es=1:p$="":rs=z 7420 retret=0: 41,0;" SELECT MODE " '''" 1 Two-dimensional vectors" '" 2 Three-dimensional vectors" !" 3 Scalar (dot) product"  " 4 Cross product"  "" 5 Scalar triple product" 6" 6 Vector equation"'"  - explanation" 6" 7 Vector equation"'"  - calculation" =" 8 Vector differentiation"'"  - explanation" @" 9 Vector and scalar products using unit vectors" " 10 Stop" B20,0;"Enter a number from 1 to 10 and press ENTER." ;m=1:t=1:o=127:p=87W:v=64@  7000X ch=i$ 6ch<1ch>10 chɺch7150:282  $7420:900+100d*ch ,1,4;"TWO-DIMENSIONAL VECTORS" -21,1;"Enter length of vector" 7000X:vl=i$ 21,7;" angle" 7000X:va=i$ ,21,0;z$:v=v+1:va=va/r o=o+m*(vl*va) p=p+m*(vl*va)  7600  7650 V20,0;"Press:I-input vector; M-multiplyvector; V-values; other-new mode" 7500L:a$=i$  /20,0;z$;z$:m<0m=1  a$="I"1010 a$="M"1090B a$"V"240 1i=((o-127)*100d+.5)/100d 0j=((p-87W)*100d+.5)/100d >rvl=((o-127)*(o-127)+(p-87W)*(p-87W)) "2o127rva=r*((p-87W)/(o-127)) $o=127rva=90Z ( o127rva=rva+180 *+o127p<87Wrva=rva+360h , 10808 .&quit=1:7400:10808 0 m=1 2a$="V"1030 7 81:1 :N2,0;" Vector sum O";v;"=";(rvl*100d+.5)/100d "19,0;" I=";i,"J=";j @0:0: B220,0;"Enter multiplication factor." D 7000X Fm=i$-1 H20,0;z$ J 1017 L:ex=0:1,3;"THREE-DIMENSIONAL VECTORS" M d=0 Pquit=1 Q!w=01.9s333*ͧ/6 Vo=127+70F*w Xp=87W+70F*w ` 7650 ed=d+30 jw lquit=0 mex=1ex=0: o*20,0;"Enter vector, part i" t7000X:i=i$ y*20,0;"Enter vector, part j" ~7000X:j=i$ *20,0;"Enter vector, part k" 7000X:k=i$ 20,0;z$  40( )1,6;"SCALAR (DOT) PRODUCT" "'" Enter length of first vector" 7000X:vl=i$ >5;1;vl;0'" Enter angle of first vector" 7000X:va=i$  va=va/r K5;1;i$;" degrees"'0'" Enter length of second vector" 7000X:vl2=i$ @5;1;vl2;0'" Enter angle of second vector" 7000X:va2=i$/r !5;1;i$;" degrees" ch=31220 ch=4 "'" Enter length of third vector" 7000X:vl3=i$ ?5;1;vl3;0'" Enter angle of third vector" 7000X:va3=i$/r !5;1;i$;" degrees" ch=5ch=6 R2'" Scalar product = ";(100d*(vl*vl2*(va2-va))+.5)/100d  7490B i$="R"288   240 "1,9 ;"CROSS-PRODUCT"  1201 cp1=(vl*vl2*(va2-va)) (c2'" Vector (cross) product = "'5;(100d*(vl*vl2*(va2-va))+.5)/100d 2 1240 x*1,5;"SCALAR TRIPLE PRODUCT"  1201 y2'" Scalar triple product = "'5;(100d*(vl*vl2*(va2-va)*vl3*(90Z/r-va3))+.5)/100d  1240 31,1;"VECTOR EQUATION - ILLUSTRATION"  ch=7 ''''" A vector equation has the form:" *2'" ve=f(t)i + g(t)j + h(t)k" >'" where: t represents a variable such as time." @'" f(t), g(t) and h(t) are functions of t."  7400 '" Suppose ve = 3i + tj + tk."'''" Then as t varies from, say, 1 to 5, the result is a series of vectors varying in direction and magnitude." X1''" The t-function may be any expression for t, including a constant." ''" An illustration follows."  7400 +ra=5:x$="10":y$="4*t":w$="2*t*t"  t=rsraes M2,16;"O";(v+1);" t=";(t*100d+.5)/100d ]19,1;"ve = ";x$;"i";("+"y$(1)"-");y$;"j";("+"w$(1)"-");w$;"k" i=x$:j=y$:k=w$  31 t "U20,0;"Press: V- enter vector equation;any other letter - change mode." ' 7500L ,i$="V"1620T 6 240 @31,1;" VECTOR EQUATION " E 1625Y J 7490B Oi$"R"240 T 7420 Y\'" Press: P - to plot points only any other letter - full diagram." ^ 7500L `p$=i$ ci$"P"p$="" fret=1:240 h'" Enter t-function, part i" m)7000X:x$=i$:6;1;x$ r'" Enter t-function, part j" w)7000X:y$=i$:6;1;y$ |'" Enter t-function, part k" )7000X:w$=i$:6;1;w$ ''" Enter t-function range; FROM:" *7000X:rs=i$:6;1;rs %'" Enter t-function range; TO:" *7000X:ra=i$:6;1;ra '" Enter step size" 7000X:es=i$ 7420:1535 +1,5;"VECTOR DIFFERENTIATION" e'" Differentiation of a vector equation is similar to that of an ordinary algebraic equation." ''" Example: the vector equation:" !'"  ve = 3i + 5tj + 2tk" '" has as its differential:" '"  dve = 0i + 5j + 4tk" 52;13 ,3;1;"___"'" dt" NJ1'" The differential is itself a vector, indicating the change of direction for each value of t of the original vector." 7400:240 /1,3;"VECTOR AND SCALAR PRODUCTS"  &''" How many vectors? Press 2 or 3." '7500L:i$"2"i$"3"1806 nv=i$  7420 '" First vector - enter:"  " i "; 7000X:i=i$:1;i  " j "; 7000X:j=i$:1;j  " k "; 7000X:k=i$:1;k  '" Second vector - enter:" " " i "; $!7000X:i1=i$:1;i1 & " j "; (!7000X:j1=i$:1;j1 * " k "; ,!7000X:k1=i$:1;k1 -nv31852< .'" Third vector - enter:" 0 " i "; 2!7000X:i2=i$:1;i2 4 " j "; 6!7000X:j2=i$:1;j2 8 " k "; :!7000X:k2=i$:1;k2 <i3=i1*k1-k*j1 >j3=i1*k-i*k1 @k3=i*j1-j*i1 B 7420 Dr" For the vectors";1'" (";i;",";j;",";k;")";0;" and"'1;" (";i1;",";j1;",";k1;")," Ih'" the vector product is:";2'" ";i3;"i ";("+ "j30);j3;"j ";("+ "k30);k3;"k" N^'" the scalar product is:";2'" ";(100d*(i*i1+j*j1+k*k1)+.5)/100d P?(i*i+j*j+k*k)=0(i1*i1+j1*j1+k1*k1)=01880X S'" angle between the vectors is:";2'" ";(100d*r*((i*i1+j*j1+k*k1)/((i*i+j*j+k*k)*(i1*i1+j1*j1+k1*k1)))+.5)/100d Xnv=21240 ]E'" With the third vector";1'" (";i2;",";j2;",";k2;")," bg" the scalar triple product is:";2'" ";(100d*(i3*i2+j3*j2+k3*k2)+.5)/100d g 1240 l0:7:7::2,4;2;6;" ";6,4;" ";3,4;" "'"  "'"  " q13 ,14;0;"ICL":"n","L":28,0:0,-28:-28,0:0,28:19,6;" ROBIN ALLOTT, 1983" v l7100:i$ vi$=""7150:7020l q=1̱i$ !i$(q)"0"i$(q)"9"7080 .(i$(q)="t"i$(q)="T")ch=77080 !i$(q)="."i$(q)="-"7080 !i$(q)=""i$(q)=""7080 !i$(q)=""i$(q)=""7080 !i$(q)="("i$(q)=")"7080 !i$(q)="+"i$(q)="^"7080 !i$(q)="*"i$(q)="/"7080 #i$(q)""7150:7020l q (i$="." i$="-"7150:7020l  sound.1}L,30  sound.5,-20   7420  '0,7;"VECTOR MATHEMATICS"   sound=1:z$(32 ) * ret=0 46:7:0:: 9 6 >00,0;z$;z$;20,0;z$;z$ @I112p,144,32 ,64@,240,0,0,0 H 8 R 7180  T/7232@:q=07:t:"a"+q,t:q W*2''" Welcome to this program." \&''" The program can run in silence." a" However, the computer can:" fl1'" - ring when input is required"''" - buzz if you make a mistake"''" - beep each key depression." k)2''6;"Do you want sound?" pI20,6;"Press S for sound;"'" any other letter for silence!" u 7500L zi$"S"sound=0  240 K20,0;z$;z$;21,1;"Press any letter to continue."  7100 =""7410 quitquit=0: q=219 7;q,0;z$ q 6;z$;z$ $2,0;: BN20,0;"Press: R - repeat mode"'"any other letter - change mode." L 7100 Vi$= `i$=""7510V ji$>"Z"i$=(i$-32 ) t20,0;z$;z$ ~ 11 ,16;"O" &126~,88X:2,-2 %126~,86V:2,2  o<1o>254p<16p>159.5,20:20,2;"Plot point off the screen - plotting ignored ...":200:20,0;z$;z$: @quit((175-p)/8),(o/8)+(o<248);v &o-1,p-1:2,2 'o-1,p+1:2,-2 >quit((175-p)/8),(o/8)+(o<248);d   &"PART 3"10 oune zuire/WlpopWv@m ijk`a,P*b,P*c],P*]dhvfvpW