Dot and Cross product A fast Maple note Worksheet by \302\251 Mike May, S.J. 2006- maymk@slu.edu We have been looking at dot products and cross products in class. It seems worthwhile to point out the syntax for doing them with Maple. (You can then use Maple as another way to check your work.) First we define a bunch of vectors: restart; a := <1, 2, 3>; b := <4, 5, 6>; v := <v1, v2, v3>; w := <w1, w2, w3>; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCInZ2Fx LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIna3Zv LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoS2hMIw== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCInS08oKg==
<Text-field style="Heading 1" layout="Heading 1">LinearAlgebra Commands</Text-field> The commands for dot product and cross product are part of the LinearAlgebra package. The syntax is: LinearAlgebra[DotProduct](vector1, vector2); LinearAlgebra[CrossProduct](vector1, vector2); LinearAlgebra[DotProduct](a, b); LinearAlgebra[CrossProduct](a, b); LinearAlgebra[DotProduct](v, w); LinearAlgebra[CrossProduct](v,w); IiNL LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCInPyIpKik= LCgqJi1JKmNvbmp1Z2F0ZUclKnByb3RlY3RlZEc2I0kjdjFHNiIiIiJJI3cxR0YpRipGKiomLUYlNiNJI3YyR0YpRipJI3cyR0YpRipGKiomLUYlNiNJI3YzR0YpRipJI3czR0YpRipGKg== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoU1R4Iw== An alternative syntax for the dot product is to put a dot (or period) between the two vectors. a.b; v.w; IiNL LCgqJi1JKmNvbmp1Z2F0ZUclKnByb3RlY3RlZEc2I0kjdjFHNiIiIiJJI3cxR0YpRipGKiomLUYlNiNJI3YyR0YpRipJI3cyR0YpRipGKiomLUYlNiNJI3YzR0YpRipJI3czR0YpRipGKg== Yet another syntax is to use the "with(LinearAlgebra):" command to load the LinearAlgebra package, then use the short form of the command. This way the package only needs to be loaded once in a Maple session. with(LinearAlgebra); 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 DotProduct(a, b); CrossProduct(a, b); DotProduct(v, w); CrossProduct(v, w);; IiNL LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoJT1eSg== LCgqJi1JKmNvbmp1Z2F0ZUclKnByb3RlY3RlZEc2I0kjdjFHNiIiIiJJI3cxR0YpRipGKiomLUYlNiNJI3YyR0YpRipJI3cyR0YpRipGKiomLUYlNiNJI3YzR0YpRipJI3czR0YpRipGKg== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIob3k7JA== Once the LinearAlgebra package has been loaded the cross product can also be called with the &x operator. a &x b; v &x w; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoO3o7JA== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoZ0c+JA==
<Text-field style="Heading 1" layout="Heading 1">Other packages with dot and cross product</Text-field> The dot and cross product are in a couple of other packages we may use. In particular they are in both the VectorCalculus and the Student[VectorCalculus] packages. As with LinearAlgebra, these commands can be loaded with the package or called with the long format. VectorCalculus[DotProduct](a,b); VectorCalculus[DotProduct](v,w); VectorCalculus[CrossProduct](a,b); VectorCalculus[CrossProduct](v,w); IiNL LCgqJkkjdjFHNiIiIiJJI3cxR0YlRiZGJiomSSN2MkdGJUYmSSN3MkdGJUYmRiYqJkkjdjNHRiVGJkkjdzNHRiVGJkYm LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIodzw0JA== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoOz00JA== Student[VectorCalculus][DotProduct](a,b); Student[VectorCalculus][DotProduct](v,w); Student[VectorCalculus][CrossProduct](a,b); Student[VectorCalculus][CrossProduct](v,w); IiNL LCgqJkkjdjFHNiIiIiJJI3cxR0YlRiZGJiomSSN2MkdGJUYmSSN3MkdGJUYmRiYqJkkjdjNHRiVGJkkjdzNHRiVGJkYm LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoO0k0JA== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIob11XJQ== The Student[LinearAlgebra] package also has a command to visualize the cross product of two vectors. Student[LinearAlgebra][CrossProductPlot](a,b); 6(-%*AXESSTYLEG6#%'NORMALG-%+AXESLABELSG6%Q"x6"Q"y6"Q"z6"-%)POLYGONSG6`o7&7%$"+k()\hN!#6$"+Fv*H7(!#6$!+t7$e$f!#67%$"+x)\hN)!#5$"+w*H7n"!"*$"+(oT1M#!"*7%$"+BhJ5))!#5$"+@q^J;!"*$"+;"y>N#!"*7%$"+=7;.")!#6$"+`>q^J!#6$!+v$)=-[!#67&7%$"+=7;.")!#6$"+`>q^J!#6$!+v$)=-[!#67%$"+BhJ5))!#5$"+@q^J;!"*$"+;"y>N#!"*7%$"+^"p\&*)!#5$"+Ncwz:!"*$"+tsl"Q#!"*7%$"+,:p\&*!#6$!+ZmVB?!#6$!+OFFM=!#67&7%$"+,:p\&*!#6$!+ZmVB?!#6$!+OFFM=!#67%$"+^"p\&*)!#5$"+Ncwz:!"*$"+tsl"Q#!"*7%$"+Bk&[t)!#5$"+*3Vd`"!"*$"+FFM=C!"*7%$"+>Uc[t!#6$!+87pDk!#6$"+OFFM=!#67&7%$"+>Uc[t!#6$!+87pDk!#6$"+OFFM=!#67%$"+Bk&[t)!#5$"+*3Vd`"!"*$"+FFM=C!"*7%$"+=N0M#)!#5$"++XE;:!"*$"+%)=-[C!"*7%$"+o^`SB!#6$!+Z,bt$)!#6$"+v$)=-[!#67&7%$"+o^`SB!#6$!+Z,bt$)!#6$"+v$)=-[!#67%$"+=N0M#)!#5$"++XE;:!"*$"+%)=-[C!"*7%$"+D,&Qk(!#5$"+E+xG:!"*$"+8$e$fC!"*7%$!+k()\hN!#6$!+Fv*H7(!#6$"+t7$e$f!#67&7%$!+k()\hN!#6$!+Fv*H7(!#6$"+t7$e$f!#67%$"+D,&Qk(!#5$"+E+xG:!"*$"+8$e$fC!"*7%$"+zQo*=(!#5$"+")H[o:!"*$"+%)=-[C!"*7%$!+=7;.")!#6$!+`>q^J!#6$"+v$)=-[!#67&7%$!+=7;.")!#6$!+`>q^J!#6$"+v$)=-[!#67%$"+zQo*=(!#5$"+")H[o:!"*$"+%)=-[C!"*7%$"+^3.Xq!#5$"+nVB?;!"*$"+FFM=C!"*7%$!+,:p\&*!#6$"+ZmVB?!#6$"+OFFM=!#67&7%$!+,:p\&*!#6$"+ZmVB?!#6$"+OFFM=!#67%$"+^3.Xq!#5$"+nVB?;!"*$"+FFM=C!"*7%$"+zN9ls!#5$"+8pDk;!"*$"+tsl"Q#!"*7%$!+>Uc[t!#6$"+87pDk!#6$!+OFFM=!#67&7%$!+>Uc[t!#6$"+87pDk!#6$!+OFFM=!#67%$"+zN9ls!#5$"+8pDk;!"*$"+tsl"Q#!"*7%$"+%[Yfw(!#5$"+-bt$o"!"*$"+;"y>N#!"*7%$!+o^`SB!#6$"+Z,bt$)!#6$!+v$)=-[!#67&7%$!+o^`SB!#6$"+Z,bt$)!#6$!+v$)=-[!#67%$"+%[Yfw(!#5$"+-bt$o"!"*$"+;"y>N#!"*7%$"+x)\hN)!#5$"+w*H7n"!"*$"+(oT1M#!"*7%$"+k()\hN!#6$"+Fv*H7(!#6$!+t7$e$f!#67%7%$"+a(*H7()!#5$"+_*fCu"!"*$"+uLG"G#!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+XAj?'*!#5$"+SS.j;!"*$"+Li&RI#!"*7%7%$"+XAj?'*!#5$"+SS.j;!"*$"+Li&RI#!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+,$Q*4**!#5$"+o7`f:!"*$"+XXJjB!"*7%7%$"+,$Q*4**!#5$"+o7`f:!"*$"+XXJjB!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+XGrp%*!#5$"+xh[r9!"*$"+baoOC!"*7%7%$"+XGrp%*!#5$"+xh[r9!"*$"+baoOC!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+Nq5o%)!#5$"+)**GDV"!"*$"+nP/'\#!"*7%7%$"+Nq5o%)!#5$"+)**GDV"!"*$"+nP/'\#!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+[-q(G(!#5$"+]+ad9!"*$"+Emr=D!"*7%7%$"+[-q(G(!#5$"+]+ad9!"*$"+Emr=D!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+dxOzj!#5$"+if'p`"!"*$"+nP/'\#!"*7%7%$"+dxOzj!#5$"+if'p`"!"*$"+nP/'\#!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+,<1!4'!#5$"+M(o/k"!"*$"+baoOC!"*7%7%$"+,<1!4'!#5$"+M(o/k"!"*$"+baoOC!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+drGIl!#5$"+DQ^G<!"*$"+XXJjB!"*7%7%$"+drGIl!#5$"+DQ^G<!"*$"+XXJjB!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+nH*=`(!#5$"+/5Zn<!"*$"+Li&RI#!"*7%7%$"+nH*=`(!#5$"+/5Zn<!"*$"+Li&RI#!"*7%$"+++++5!"*$"+++++?!"*$"+++++I!"*7%$"+a(*H7()!#5$"+_*fCu"!"*$"+uLG"G#!"*7,7%$"+a(*H7()!#5$"+_*fCu"!"*$"+uLG"G#!"*7%$"+XAj?'*!#5$"+SS.j;!"*$"+Li&RI#!"*7%$"+,$Q*4**!#5$"+o7`f:!"*$"+XXJjB!"*7%$"+XGrp%*!#5$"+xh[r9!"*$"+baoOC!"*7%$"+Nq5o%)!#5$"+)**GDV"!"*$"+nP/'\#!"*7%$"+[-q(G(!#5$"+]+ad9!"*$"+Emr=D!"*7%$"+dxOzj!#5$"+if'p`"!"*$"+nP/'\#!"*7%$"+,<1!4'!#5$"+M(o/k"!"*$"+baoOC!"*7%$"+drGIl!#5$"+DQ^G<!"*$"+XXJjB!"*7%$"+nH*=`(!#5$"+/5Zn<!"*$"+Li&RI#!"*7,7%$"+k()\hN!#6$"+Fv*H7(!#6$!+t7$e$f!#67%$"+=7;.")!#6$"+`>q^J!#6$!+v$)=-[!#67%$"+,:p\&*!#6$!+ZmVB?!#6$!+OFFM=!#67%$"+>Uc[t!#6$!+87pDk!#6$"+OFFM=!#67%$"+o^`SB!#6$!+Z,bt$)!#6$"+v$)=-[!#67%$!+k()\hN!#6$!+Fv*H7(!#6$"+t7$e$f!#67%$!+=7;.")!#6$!+`>q^J!#6$"+v$)=-[!#67%$!+,:p\&*!#6$"+ZmVB?!#6$"+OFFM=!#67%$!+>Uc[t!#6$"+87pDk!#6$!+OFFM=!#67%$!+o^`SB!#6$"+Z,bt$)!#6$!+v$)=-[!#67&7%$"+.PiUU!#6$"+I'zKI&!#6$!+#\:yC(!#67%$"+PiUUK!"*$"+'zKI0%!"*$"+X=_FZ!"*7%$"+fA"*zK!"*$"+kMV1S!"*$"+TROTZ!"*7%$"+**eA"*z!#6$"*ojMV'!#6$!+/fgje!#67&7%$"+**eA"*z!#6$"*ojMV'!#6$!+/fgje!#67%$"+fA"*zK!"*$"+kMV1S!"*$"+TROTZ!"*7%$"+9X(oG$!"*$"+nnPdR!"*$"+=IgxZ!"*7%$"+69X(o)!#6$!+ULKiU!#6$!+b")pRA!#67&7%$"+69X(o)!#6$!+ULKiU!#6$!+b")pRA!#67%$"+9X(oG$!"*$"+nnPdR!"*$"+=IgxZ!"*7%$"+eOlgK!"*$"+'p+Y#R!"*$"+#)pRA[!"*7%$"+ndOlg!#6$!+)RI*Rv!#6$"+b")pRA!#67&7%$"+ndOlg!#6$!+)RI*Rv!#6$"+b")pRA!#67%$"+eOlgK!"*$"+'p+Y#R!"*$"+#)pRA[!"*7%$"+l^E6K!"*$"+(fC1#R!"*$"+fgje[!"*7%$"+Zl^E6!#6$!+C.aPz!#6$"+/fgje!#67&7%$"+Zl^E6!#6$!+C.aPz!#6$"+/fgje!#67%$"+l^E6K!"*$"+(fC1#R!"*$"+fgje[!"*7%$"+jPddJ!"*$"+/s'p%R!"*$"+b"yC([!"*7%$!+.PiUU!#6$!+I'zKI&!#6$"+#\:yC(!#67&7%$!+.PiUU!#6$!+I'zKI&!#6$"+#\:yC(!#67%$"+jPddJ!"*$"+/s'p%R!"*$"+b"yC([!"*7%$"+Tx3?J!"*$"+Olc$*R!"*$"+fgje[!"*7%$!+**eA"*z!#6$!*ojMV'!#6$"+/fgje!#67&7%$!+**eA"*z!#6$!*ojMV'!#6$"+/fgje!#67%$"+Tx3?J!"*$"+Olc$*R!"*$"+fgje[!"*7%$"+'[DJ6$!"*$"+LKiUS!"*$"+#)pRA[!"*7%$!+69X(o)!#6$"+ULKiU!#6$"+b")pRA!#67&7%$!+69X(o)!#6$"+ULKiU!#6$"+b")pRA!#67%$"+'[DJ6$!"*$"+LKiUS!"*$"+#)pRA[!"*7%$"+UjMRJ!"*$"+/$*RvS!"*$"+=IgxZ!"*7%$!+ndOlg!#6$"+)RI*Rv!#6$!+b")pRA!#67&7%$!+ndOlg!#6$"+)RI*Rv!#6$!+b")pRA!#67%$"+UjMRJ!"*$"+/$*RvS!"*$"+=IgxZ!"*7%$"+N[t)=$!"*$"+.aPzS!"*$"+TROTZ!"*7%$!+Zl^E6!#6$"+C.aPz!#6$!+/fgje!#67&7%$!+Zl^E6!#6$"+C.aPz!#6$!+/fgje!#67%$"+N[t)=$!"*$"+.aPzS!"*$"+TROTZ!"*7%$"+PiUUK!"*$"+'zKI0%!"*$"+X=_FZ!"*7%$"+.PiUU!#6$"+I'zKI&!#6$!+#\:yC(!#67%7%$"+uC&[G$!"*$"+$flg5%!"*$"+!pV]l%!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+=X#)fL!"*$"+Fp'G,%!"*$"+#)ys#o%!"*7%7%$"+=X#)fL!"*$"+Fp'G,%!"*$"+#)ys#o%!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+G!\PP$!"*$"+LNv9R!"*$"+Pg?bZ!"*7%7%$"+G!\PP$!"*$"+LNv9R!"*$"+Pg?bZ!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+:tI@L!"*$"+#R,#\Q!"*$"+jRzW[!"*7%7%$"+:tI@L!"*$"+#R,#\Q!"*$"+jRzW[!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+J.`AK!"*$"+%>\7%Q!"*$"+=@F<\!"*7%7%$"+J.`AK!"*$"+%>\7%Q!"*$"+=@F<\!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+Ev9:J!"*$"+2W$R*Q!"*$"+5j&\%\!"*7%7%$"+Ev9:J!"*$"+2W$R*Q!"*$"+5j&\%\!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+#[v,/$!"*$"+tI8()R!"*$"+=@F<\!"*7%7%$"+#[v,/$!"*$"+tI8()R!"*$"+=@F<\!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+s4DEI!"*$"+nkC&3%!"*$"+jRzW[!"*7%7%$"+s4DEI!"*$"+nkC&3%!"*$"+jRzW[!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+&o#pyI!"*$"+3')z]T!"*$"+Pg?bZ!"*7%7%$"+&o#pyI!"*$"+3')z]T!"*$"+Pg?bZ!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+p'pu<$!"*$"+13veT!"*$"+#)ys#o%!"*7%7%$"+p'pu<$!"*$"+13veT!"*$"+#)ys#o%!"*7%$"+********R!"*$"+++++]!"*$"+++++g!"*7%$"+uC&[G$!"*$"+$flg5%!"*$"+!pV]l%!"*7,7%$"+uC&[G$!"*$"+$flg5%!"*$"+!pV]l%!"*7%$"+=X#)fL!"*$"+Fp'G,%!"*$"+#)ys#o%!"*7%$"+G!\PP$!"*$"+LNv9R!"*$"+Pg?bZ!"*7%$"+:tI@L!"*$"+#R,#\Q!"*$"+jRzW[!"*7%$"+J.`AK!"*$"+%>\7%Q!"*$"+=@F<\!"*7%$"+Ev9:J!"*$"+2W$R*Q!"*$"+5j&\%\!"*7%$"+#[v,/$!"*$"+tI8()R!"*$"+=@F<\!"*7%$"+s4DEI!"*$"+nkC&3%!"*$"+jRzW[!"*7%$"+&o#pyI!"*$"+3')z]T!"*$"+Pg?bZ!"*7%$"+p'pu<$!"*$"+13veT!"*$"+#)ys#o%!"*7,7%$"+.PiUU!#6$"+I'zKI&!#6$!+#\:yC(!#67%$"+**eA"*z!#6$"*ojMV'!#6$!+/fgje!#67%$"+69X(o)!#6$!+ULKiU!#6$!+b")pRA!#67%$"+ndOlg!#6$!+)RI*Rv!#6$"+b")pRA!#67%$"+Zl^E6!#6$!+C.aPz!#6$"+/fgje!#67%$!+.PiUU!#6$!+I'zKI&!#6$"+#\:yC(!#67%$!+**eA"*z!#6$!*ojMV'!#6$"+/fgje!#67%$!+69X(o)!#6$"+ULKiU!#6$"+b")pRA!#67%$!+ndOlg!#6$"+)RI*Rv!#6$!+b")pRA!#67%$!+Zl^E6!#6$"+C.aPz!#6$!+/fgje!#67&7%$"+3kU8=!#6$!+:G&oi$!#6$!+S?8n!*!#67%$!+Od'=Q#!"*$"+r9tjZ!"*$!+>8n!\#!"*7%$!+!f5JL#!"*$"+%Qnnz%!"*$!+QYNtC!"*7%$"+v4%*)o'!#6$!*m9EB$!#6$!+5RYNt!#67&7%$"+v4%*)o'!#6$!*m9EB$!#6$!+5RYNt!#67%$!+!f5JL#!"*$"+%Qnnz%!"*$!+QYNtC!"*7%$!+E\!*4B!"*$"+Z!Q5$[!"*$!+y*=!GC!"*7%$"+Pu]4!*!#6$"+wZ!Q5$!#6$!+&)y*=!G!#67&7%$"+Pu]4!*!#6$"+wZ!Q5$!#6$!+&)y*=!G!#67%$!+E\!*4B!"*$"+Z!Q5$[!"*$!+y*=!GC!"*7%$!+<D6@B!"*$"+IKX`[!"*$!+?5)>P#!"*7%$"+$G[())y!#6$"+%3B`M&!#6$"+&)y*=!G!#67&7%$"+$G[())y!#6$"+%3B`M&!#6$"+&)y*=!G!#67%$!+<D6@B!"*$"+IKX`[!"*$!+?5)>P#!"*7%$!+YCXiB!"*$"+'4^a&[!"*$!+g`kEB!"*7%$"+6avaP!#6$"+g'4^a&!#6$"+5RYNt!#67&7%$"+6avaP!#6$"+g'4^a&!#6$"+5RYNt!#67%$!+YCXiB!"*$"+'4^a&[!"*$!+g`kEB!"*7%$!+kU8=C!"*$"+F&oi$[!"*$!+z'G$4B!"*7%$!+3kU8=!#6$"+:G&oi$!#6$"+S?8n!*!#67&7%$!+3kU8=!#6$"+:G&oi$!#6$"+S?8n!*!#67%$!+kU8=C!"*$"+F&oi$[!"*$!+z'G$4B!"*7%$!+5%*)oY#!"*$"+9EB.[!"*$!+g`kEB!"*7%$!+v4%*)o'!#6$"*m9EB$!#6$"+5RYNt!#67&7%$!+v4%*)o'!#6$"*m9EB$!#6$"+5RYNt!#67%$!+5%*)oY#!"*$"+9EB.[!"*$!+g`kEB!"*7%$!+u]4!\#!"*$"+^>'*oZ!"*$!+?5)>P#!"*7%$!+Pu]4!*!#6$!+wZ!Q5$!#6$"+&)y*=!G!#67&7%$!+Pu]4!*!#6$!+wZ!Q5$!#6$"+&)y*=!G!#67%$!+u]4!\#!"*$"+^>'*oZ!"*$!+?5)>P#!"*7%$!+$[())yC!"*$"+onaYZ!"*$!+y*=!GC!"*7%$!+$G[())y!#6$!+%3B`M&!#6$!+&)y*=!G!#67&7%$!+$G[())y!#6$!+%3B`M&!#6$!+&)y*=!G!#67%$!+$[())yC!"*$"+onaYZ!"*$!+y*=!GC!"*7%$!+avaPC!"*$"+-*[Xu%!"*$!+QYNtC!"*7%$!+6avaP!#6$!+g'4^a&!#6$!+5RYNt!#67&7%$!+6avaP!#6$!+g'4^a&!#6$!+5RYNt!#67%$!+avaPC!"*$"+-*[Xu%!"*$!+QYNtC!"*7%$!+Od'=Q#!"*$"+r9tjZ!"*$!+>8n!\#!"*7%$"+3kU8=!#6$!+:G&oi$!#6$!+S?8n!*!#67%7%$!+s9tjB!"*$"+VHYFZ!"*$!+SEM"e#!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+!=@iE#!"*$"+qZ`$z%!"*$!+x#4na#!"*7%7%$!+!=@iE#!"*$"+qZ`$z%!"*$!+x#4na#!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+^)4)>A!"*$"+&4w?'[!"*$!+dz.cC!"*7%7%$!+^)4)>A!"*$"+&4w?'[!"*$!+dz.cC!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+M]AUA!"*$"+hk!p!\!"*$!+T?'RM#!"*7%7%$!+M]AUA!"*$"+hk!p!\!"*$!+T?'RM#!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+#*[!\K#!"*$"+#>-4"\!"*$!+@2H`A!"*7%7%$!+#*[!\K#!"*$"+#>-4"\!"*$!+@2H`A!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+G&oiV#!"*$"+bq`s[!"*$!+etl=A!"*7%7%$!+G&oiV#!"*$"+bq`s[!"*$!+etl=A!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+?)yP`#!"*$"+G_Y1[!"*$!+@2H`A!"*7%7%$!+?)yP`#!"*$"+G_Y1[!"*$!+@2H`A!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+\,>!e#!"*$"+.R#zt%!"*$!+T?'RM#!"*7%7%$!+\,>!e#!"*$"+.R#zt%!"*$!+T?'RM#!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+m\xdD!"*$"+PN4$p%!"*$!+dz.cC!"*7%7%$!+m\xdD!"*$"+PN4$p%!"*$!+dz.cC!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+3^4vC!"*$"+1y4*o%!"*$!+x#4na#!"*7%7%$!+3^4vC!"*$"+1y4*o%!"*$!+x#4na#!"*7%$!+++++I!"*$"+++++g!"*$!+********H!"*7%$!+s9tjB!"*$"+VHYFZ!"*$!+SEM"e#!"*7,7%$!+s9tjB!"*$"+VHYFZ!"*$!+SEM"e#!"*7%$!+!=@iE#!"*$"+qZ`$z%!"*$!+x#4na#!"*7%$!+^)4)>A!"*$"+&4w?'[!"*$!+dz.cC!"*7%$!+M]AUA!"*$"+hk!p!\!"*$!+T?'RM#!"*7%$!+#*[!\K#!"*$"+#>-4"\!"*$!+@2H`A!"*7%$!+G&oiV#!"*$"+bq`s[!"*$!+etl=A!"*7%$!+?)yP`#!"*$"+G_Y1[!"*$!+@2H`A!"*7%$!+\,>!e#!"*$"+.R#zt%!"*$!+T?'RM#!"*7%$!+m\xdD!"*$"+PN4$p%!"*$!+dz.cC!"*7%$!+3^4vC!"*$"+1y4*o%!"*$!+x#4na#!"*7,7%$"+3kU8=!#6$!+:G&oi$!#6$!+S?8n!*!#67%$"+v4%*)o'!#6$!*m9EB$!#6$!+5RYNt!#67%$"+Pu]4!*!#6$"+wZ!Q5$!#6$!+&)y*=!G!#67%$"+$G[())y!#6$"+%3B`M&!#6$"+&)y*=!G!#67%$"+6avaP!#6$"+g'4^a&!#6$"+5RYNt!#67%$!+3kU8=!#6$"+:G&oi$!#6$"+S?8n!*!#67%$!+v4%*)o'!#6$"*m9EB$!#6$"+5RYNt!#67%$!+Pu]4!*!#6$!+wZ!Q5$!#6$"+&)y*=!G!#67%$!+$G[())y!#6$!+%3B`M&!#6$!+&)y*=!G!#67%$!+6avaP!#6$!+g'4^a&!#6$!+5RYNt!#6-%&STYLEG6#%,PATCHNOGRIDG-%&COLORG6cw%$RGBG$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$""!!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""$"#5!""$""!!""$"#5!""-%&TITLEG6#Q?The~Cross~Product~of~2~Vectors6"-%(SCALINGG6#%,CONSTRAINEDG-%,ORIENTATIONG6$$!$5(!""$!$![!""
TTdSMApJM1JUQUJMRV9TQVZFLzcwNTQ2MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiIiIiIyIiJEYmTTdSMApJM1JUQUJMRV9TQVZFLzY4NzU2NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiJSIiJiIiJ0YmTTdSMApJNFJUQUJMRV9TQVZFLzIzMzYxMzJYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIkIiQlI3YxRyUjdjJHJSN2M0dGJg==TTdSMApJM1JUQUJMRV9TQVZFLzk3MzYzMlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCUjdzFHJSN3MkclI3czR0YmTTdSMApJM1JUQUJMRV9TQVZFLzg5ODEyMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCEiJCIiJ0YnRiY=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TTdSMApJNFJUQUJMRV9TQVZFLzMwOTE4MTZYKiUpYW55dGhpbmdHNiI2Iy8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCYqJiUjdjJHIiIiJSN3M0dGLUYtKiYlI3YzR0YtJSN3MkdGLSEiIiwmKiZGMEYtJSN3MUdGLUYtKiYlI3YxR0YtRi5GLUYyLCYqJkY3Ri1GMUYtRi0qJkYsRi1GNUYtRjI2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzMwOTMwMTZYKiUpYW55dGhpbmdHNiI2Iy8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkISIkIiInRio2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzQ0NDUwNjhYKiUpYW55dGhpbmdHNiI2Iy8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCYqJiUjdjJHIiIiJSN3M0dGLUYtKiYlI3YzR0YtJSN3MkdGLSEiIiwmKiZGMEYtJSN3MUdGLUYtKiYlI3YxR0YtRi5GLUYyLCYqJkY3Ri1GMUYtRi0qJkYsRi1GNUYtRjI2Ig==