LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Philosophy: The philosophy is this worksheet is to first solidify the students' understanding of the structure of a parameterization of a line and the vector equation of a plane. For this reason, "unenlightening" names have been used for various quantities in the code -- so as not to give the students a big hint. We welcome comments on whether the students would be better served to have such a hint and how to strike a balance (as well as any other comments, of course). Please send comments to symington_mf(at)mercer.edu. Lines and planes by Curtis Herink, Jawahar Pathak, and Margaret Symington Lines The most convenient way to define a line in 3-space is parametrically -- with a nice parameterization! Think of starting at a point and then moving along a line. You can move forward and backward from that point in the direction of a vector. This leads to the parametrization <A,B,C> + t* <a,b,c> ,or v1 + t *v2 with v1 = <A,B,C> and v2=<a,b,c>. Other ways of expressing this parameterization are: < A+a*t , B+b*t , C+c*t > or x = A+a*t, y = B+b*t, z = C+c*t . Run the following code with a variety of choices for the values of the constants A,B,C and a,b,c until you understand what they mean. QyRJKHJlc3RhcnRHJSpwcm90ZWN0ZWRHIiIi with(plots); with(Student[VectorCalculus])

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

Warning, inserted missing semicolon at end of statement

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

QyY+SSN2MUc2Ii1JJDwsPkdGJTYlSSJBR0YlSSJCR0YlSSJDR0YlISIiPkkjdjJHRiUtRic2JUkiYUdGJUkiYkdGJUkiY0dGJUYs Qy4+SSJBRzYiIiIkISIiPkkiQkdGJSIiI0YnPkkiQ0dGJSIiJkYnPkkiYUdGJS1JIi1HNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JUYzRjMvRjVJKFN0dWRlbnRHSShfc3lzbGliR0YlNiNGKkYnPkkiYkdGJUYmRic+SSJjR0YlIiIlRic= line1 := spacecurve(v1+t*v2, t = -5 .. 5, color = blue)

Warning, inserted missing semicolon at end of statement

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

vect1 := arrow(v1,v2,width = 0.4, head_width=1.5, color = black): point1:=pointplot3d(v1,color=red,symbol=circle): display3d({vect1,line1,point1},axes=boxed,scaling=CONSTRAINED,labels=[x,y,z]);

6+-I'CURVESG6$%*protectedGI(_syslibG6"6$7T7%$"#8""!$!#8""!$!#:""!7%$"+tO=f7!")$!+5bxQ7!")$!+ZtO=9!")7%$"+ZtO=7!")$!+?5bx6!")$!+%pMnL"!")7%$"+?5bx6!")$!+IlK;6!")$!+S?5b7!")7%$"+%pMn8"!")$!+S?5b5!")$!+(QpM<"!")7%$"+n$=f4"!")$!+0bxQ**!"*$!+Mn$=4"!")7%$"+S?5b5!")$!+11`E$*!"*$!+"3/-,"!")7%$"+9dG95!")$!+2dG9()!"*$!+wUr&G*!"*7%$"+sQpM(*!"*$!+33/-")!"*$!+WxQp%)!"*7%$"+11`E$*!"*$!+4fz*[(!"*$!+771`w!"*7%$"+StO=*)!"*$!+55bxo!"*$!+!oMn$o!"*7%$"+uS?5&)!"*$!+6hIli!"*$!+["3/-'!"*7%$"+33/-")!"*$!+771`c!"*$!+;;3/_!"*7%$"+Uv(Qp(!"*$!+8j"3/&!"*$!+%3bxQ%!"*7%$"+wUr&G(!"*$!+99dGW!"*$!+_&G9d$!"*7%$"+55bxo!"*$!+:lK;Q!"*$!+??5bF!"*7%$"+WxQpk!"*$!+;;3/K!"*$!+)[v(Q>!"*7%$"+yWAhg!"*$!+<n$=f#!"*$!+c*[C7"!"*7%$"+771`c!"*$!+==fz>!"*$!+SUAhI!#57%$"+Yz*[C&!"*$!+>pMn8!"*$"+!3T?5&!#57%$"+"oMn$[!"*$!+4--^v!#5$"+R1`E8!"*7%$"+:9dGW!"*$!+G7dG9!#5$"+qr&G9#!"*7%$"+]"3/-%!"*$"+`x(Qp%!#5$"++P=fH!"*7%$"+%)[C7O!"*$"+tEj"3"!"*$"+J-^vP!"*7%$"+>;3/K!"*$"+sv(Qp"!"*$"+in$=f%!"*7%$"+a$=fz#!"*$"+qC71B!"*$"+$Hj"3a!"*7%$"+)3bxQ#!"*$"+otO=H!"*$"+C)*[Ci!"*7%$"+B=fz>!"*$"+mAhIN!"*$"+aj"3/(!"*7%$"+d&G9d"!"*$"+kr&G9%!"*$"+&)G9dy!"*7%$"+#HlK;"!"*$"+i?5bZ!"*$"+;%pMn)!"*7%$"+g--^v!#5$"+hpMn`!"*$"+[fz*[*!"*7%$"++wQpM!#5$"+g=fzf!"*$"+[AhI5!")7%$!++1XAh!#6$"+fn$=f'!"*$"+,\C76!")7%$!+?x(Qp%!#5$"+e;3/s!"*$"+av(Q>"!")7%$!+!Q5bx)!#5$"+dlK;y!"*$"+3-^v7!")7%$!+/Vr&G"!"*$"+c9dG%)!"*$"+hG9d8!")7%$!+qv(Qp"!"*$"+bj"3/*!"*$"+9bxQ9!")7%$!+O3/-@!"*$"+a71`'*!"*$"+n"3/_"!")7%$!+-T?5D!"*$"+:1`E5!")$"+?3/-;!")7%$!+otO=H!"*$"+0^v(3"!")$"+uMn$o"!")7%$!+M1`EL!"*$"+&fz*[6!")$"+FhIl<!")7%$!++RpMP!"*$"+&3/-@"!")$"+!yQp%=!")7%$!+mr&G9%!"*$"+v&G9F"!")$"+L9dG>!")7%$!+K/-^X!"*$"+lIlK8!")$"+'3/-,#!")7%$!+)p$=f\!"*$"+bv(QR"!")$"+Sn$=4#!")7%$!+kpMn`!"*$"+X?5b9!")$"+$RpM<#!")7%$!+I-^vd!"*$"+MlK;:!")$"+Y?5bA!")7%$!+'\tO='!"*$"+C5bx:!")$"+*pMnL#!")7%$!+in$=f'!"*$"+9bxQ;!")$"+_tO=C!")7%$!+G+++q!"*$"+/+++<!")$"+1+++D!")-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"$""!""!$""!""!$"*++++"!")-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7&7%$"+3ef<H!"*$"+*G1O7#!"*$"+(=$4m[!"*7%$"+3ef<8!"*$"+*G1O_%!"*$"+(=$4m!)!"*7%$"+')p9J9!"*$"+2&3_c%!"*$"+8rm"4)!"*7%$"+')p9JI!"*$"+2&3_;#!"*$"+8rm"*[!"*7&7%$"+')p9JI!"*$"+2&3_;#!"*$"+8rm"*[!"*7%$"+')p9J9!"*$"+2&3_c%!"*$"+8rm"4)!"*7%$"+v5!G`"!"*$"+"p1Pa%!"*$"+>0ie")!"*7%$"+v5!G8$!"*$"+"p1P9#!"*$"+>0ie\!"*7&7%$"+v5!G8$!"*$"+"p1P9#!"*$"+>0ie\!"*7%$"+v5!G`"!"*$"+"p1Pa%!"*$"+>0ie")!"*7%$"+n'HPe"!"*$"+/QJnW!"*$"+"[z8C)!"*7%$"+n'HP=$!"*$"+/QJn?!"*$"+"[z8/&!"*7&7%$"+n'HP=$!"*$"+/QJn?!"*$"+"[z8/&!"*7%$"+n'HPe"!"*$"+/QJnW!"*$"+"[z8C)!"*7%$"+r(zWc"!"*$"+J$4_O%!"*$"+()GL3$)!"*7%$"+r(zW;$!"*$"+J$4_'>!"*$"+()GL3^!"*7&7%$"+r(zW;$!"*$"+J$4_'>!"*$"+()GL3^!"*7%$"+r(zWc"!"*$"+J$4_O%!"*$"+()GL3$)!"*7%$"+#>/C["!"*$"+6PRwU!"*$"+8o!RL)!"*7%$"+#>/C3$!"*$"+6PRw=!"*$"+8o!R8&!"*7&7%$"+#>/C3$!"*$"+6PRw=!"*$"+8o!R8&!"*7%$"+#>/C["!"*$"+6PRwU!"*$"+8o!RL)!"*7%$"+9I&)o8!"*$"+$\"zMU!"*$"+()GL3$)!"*7%$"+9I&)oH!"*$"+$\"zM=!"*$"+()GL3^!"*7&7%$"+9I&)oH!"*$"+$\"zM=!"*$"+()GL3^!"*7%$"+9I&)o8!"*$"+$\"zMU!"*$"+()GL3$)!"*7%$"+D*)>n7!"*$"+4LHcU!"*$"+"[z8C)!"*7%$"+D*)>nG!"*$"+4LHc=!"*$"+"[z8/&!"*7&7%$"+D*)>nG!"*$"+4LHc=!"*$"+"[z8/&!"*7%$"+D*)>n7!"*$"+4LHcU!"*$"+"[z8C)!"*7%$"+L.F;7!"*$"+'>'oKV!"*$"+>0ie")!"*7%$"+L.F;G!"*$"+'>'oK>!"*$"+>0ie\!"*7&7%$"+L.F;G!"*$"+'>'oK>!"*$"+>0ie\!"*7%$"+L.F;7!"*$"+'>'oKV!"*$"+>0ie")!"*7%$"+H-_N7!"*$"+p1zMW!"*$"+8rm"4)!"*7%$"+H-_NG!"*$"+p1zM?!"*$"+8rm"*[!"*7&7%$"+H-_NG!"*$"+p1zM?!"*$"+8rm"*[!"*7%$"+H-_N7!"*$"+p1zMW!"*$"+8rm"4)!"*7%$"+3ef<8!"*$"+*G1O_%!"*$"+(=$4m!)!"*7%$"+3ef<H!"*$"+*G1O7#!"*$"+(=$4m[!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7%7%$"+yU)44"!"*$"+#eBN'[!"*$"+_%\yp(!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+*>,o^"!"*$"+->`>]!"*$"+t;v$z(!"*7%7%$"+*>,o^"!"*$"+->`>]!"*$"+t;v$z(!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+KS+)*=!"*$"+"4+*Q\!"*$"+Zp#[/)!"*7%7%$"+KS+)*=!"*$"+"4+*Q\!"*$"+Zp#[/)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+]i)*)3#!"*$"+jnU_Y!"*$"+`I<b$)!"*7%7%$"+]i)*)3#!"*$"+jnU_Y!"*$"+`I<b$)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+R"*z;?!"*$"+"*\`pU!"*$"+F$[ig)!"*7%7%$"+R"*z;?!"*$"+"*\`pU!"*$"+F$[ig)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+Ad,4<!"*$"+=kZOR!"*$"+[0:-()!"*7%7%$"+Ad,4<!"*$"+=kZOR!"*$"+[0:-()!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+,))>$G"!"*$"+)4o/y$!"*$"+F$[ig)!"*7%7%$"+,))>$G"!"*$"+)4o/y$!"*$"+F$[ig)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"*of*>!*!"*$"+4**4hQ!"*$"+`I<b$)!"*7%7%$"*of*>!*!"*$"+4**4hQ!"*$"+`I<b$)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"*]P,6(!"*$"+PKdZT!"*$"+Zp#[/)!"*7%7%$"*]P,6(!"*$"+PKdZT!"*$"+Zp#[/)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"*h3?$y!"*$"+4]YIX!"*$"+t;v$z(!"*7%7%$"*h3?$y!"*$"+4]YIX!"*$"+t;v$z(!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+yU)44"!"*$"+#eBN'[!"*$"+_%\yp(!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+yU)44"!"*$"+#eBN'[!"*$"+_%\yp(!"*7%$"+*>,o^"!"*$"+->`>]!"*$"+t;v$z(!"*7%$"+KS+)*=!"*$"+"4+*Q\!"*$"+Zp#[/)!"*7%$"+]i)*)3#!"*$"+jnU_Y!"*$"+`I<b$)!"*7%$"+R"*z;?!"*$"+"*\`pU!"*$"+F$[ig)!"*7%$"+Ad,4<!"*$"+=kZOR!"*$"+[0:-()!"*7%$"+,))>$G"!"*$"+)4o/y$!"*$"+F$[ig)!"*7%$"*of*>!*!"*$"+4**4hQ!"*$"+`I<b$)!"*7%$"*]P,6(!"*$"+PKdZT!"*$"+Zp#[/)!"*7%$"*h3?$y!"*$"+4]YIX!"*$"+t;v$z(!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+3ef<H!"*$"+*G1O7#!"*$"+(=$4m[!"*7%$"+')p9JI!"*$"+2&3_;#!"*$"+8rm"*[!"*7%$"+v5!G8$!"*$"+"p1P9#!"*$"+>0ie\!"*7%$"+n'HP=$!"*$"+/QJn?!"*$"+"[z8/&!"*7%$"+r(zW;$!"*$"+J$4_'>!"*$"+()GL3^!"*7%$"+#>/C3$!"*$"+6PRw=!"*$"+8o!R8&!"*7%$"+9I&)oH!"*$"+$\"zM=!"*$"+()GL3^!"*7%$"+D*)>nG!"*$"+4LHc=!"*$"+"[z8/&!"*7%$"+L.F;G!"*$"+'>'oK>!"*$"+>0ie\!"*7%$"+H-_NG!"*$"+p1zM?!"*$"+8rm"*[!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I'POINTSG6$%*protectedGI(_syslibG6"6%7%$""$""!$""#""!$""&""!-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"$"*++++"!")$""!""!$""!""!-I'SYMBOLG6$%*protectedGI(_syslibG6"6#I'CIRCLEG6$%*protectedGI(_syslibG6"-I*AXESSTYLEG6$%*protectedGI(_syslibG6"6#I$BOXG6$%*protectedGI(_syslibG6"-I(SCALINGG6"6#I,CONSTRAINEDG6$%*protectedGI(_syslibG6"-I+AXESLABELSG6$%*protectedGI(_syslibG6"6%I"xG6"I"yG6"I"zG6"

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn 1. Plot a line with tangent vector <6,-1,3> that passes through the point (4,4,-7). Show the tangent vector on your plot. 2. Graph a line through the points (4,-5,1) and (6,1,-2) by modifying the above code slightly. 3. Describe, in your own words, the meaning of the vectors v1=<A,B,C> and v2=<a,b,c>. Planes There is are a few convenient ways to define a plane in 3-space. First, we can generalize our approach to lines. The simplest way to parameterize a plane is as: <A,B,C> + s*<a,b,c> + t*<e,f,g>. It is crucial to understand the meaning of the constants that appear in the above expression. Explore the effect of changing their values in the following code. Qyg+SSN2MUc2Ii1JJDwsPkdGJTYlSSJBR0YlSSJCR0YlSSJDR0YlISIiPkkjdjJHRiUtRic2JUkiYUdGJUkiYkdGJUkiY0dGJUYsPkkjdjNHRiUtRic2JUkiZUdGJUkiZkdGJUkiZ0dGJUYs QzQ+SSJBRzYiIiIkISIiPkkiQkdGJSIiI0YnPkkiQ0dGJSIiJkYnPkkiYUdGJS1JIi1HNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JUYzRjMvRjVJKFN0dWRlbnRHSShfc3lzbGliR0YlNiNGKkYnPkkiYkdGJUYmRic+SSJjR0YlIiIlRic+SSJlR0YlIiIiRic+SSJmR0YlRkNGJz5JImdHRiUtRjE2I0ZDRic= point1:=pointplot3d(v1,color=red,symbol=circle): param1:=v1+s*v2+t*v3: plane1:=plot3d(param1,s=-2..2,t=-2..2): vect1:=arrow(v1,v2,width = 0.25, head_width=0.8,color=black): vect2 := arrow(v1,v3,width = 0.25, head_width=0.8, color = black): display([vect1,vect2,plane1,point1],axes=boxed,scaling=CONSTRAINED);

6.-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7&7%$"+!Q(\[H!"*$"+IRDx?!"*$"+U#3j"\!"*7%$"+!Q(\[8!"*$"+IRDxW!"*$"+U#3j6)!"*7%$"+moY>9!"*$"+<`D.X!"*$"+Y>HK")!"*7%$"+moY>I!"*$"+<`D.@!"*$"+Y>HK\!"*7&7%$"+moY>I!"*$"+<`D.@!"*$"+Y>HK\!"*7%$"+moY>9!"*$"+<`D.X!"*$"+Y>HK")!"*7%$"+s1+$["!"*$"+#o;)*[%!"*$"+Dy8u")!"*7%$"+s1+$3$!"*$"+#o;)*3#!"*$"+Dy8u\!"*7&7%$"+s1+$3$!"*$"+#o;)*3#!"*$"+Dy8u\!"*7%$"+s1+$["!"*$"+#o;)*[%!"*$"+Dy8u")!"*7%$"+U5$[^"!"*$"+F62UW!"*$"+v@'eA)!"*7%$"+U5$[6$!"*$"+F62U?!"*$"+v@'e-&!"*7&7%$"+U5$[6$!"*$"+F62U?!"*$"+v@'e-&!"*7%$"+U5$[^"!"*$"+F62UW!"*$"+v@'eA)!"*7%$"+d)*z-:!"*$"+KeDyV!"*$"+a!3xE)!"*7%$"+d)*z-J!"*$"+KeDy>!"*$"+a!3x1&!"*7&7%$"+d)*z-J!"*$"+KeDy>!"*$"+a!3x1&!"*7%$"+d)*z-:!"*$"+KeDyV!"*$"+a!3xE)!"*7%$"+?E]^9!"*$"+qguAV!"*$"+e<p$G)!"*7%$"+?E]^I!"*$"+qguA>!"*$"+e<p$3&!"*7&7%$"+?E]^I!"*$"+qguA>!"*$"+e<p$3&!"*7%$"+?E]^9!"*$"+qguAV!"*$"+e<p$G)!"*7%$"+MJ`!Q"!"*$"+$oWnH%!"*$"+a!3xE)!"*7%$"+MJ`!)H!"*$"+$oWn*=!"*$"+a!3x1&!"*7&7%$"+MJ`!)H!"*$"+$oWn*=!"*$"+a!3x1&!"*7%$"+MJ`!Q"!"*$"+$oWnH%!"*$"+a!3xE)!"*7%$"+G$**pJ"!"*$"+=L=5V!"*$"+v@'eA)!"*7%$"+G$**p"H!"*$"+=L=5>!"*$"+v@'e-&!"*7&7%$"+G$**p"H!"*$"+=L=5>!"*$"+v@'e-&!"*7%$"+G$**pJ"!"*$"+=L=5V!"*$"+v@'eA)!"*7%$"+e*o^G"!"*$"+t)GzN%!"*$"+Dy8u")!"*7%$"+e*o^)G!"*$"+t)Gz&>!"*$"+Dy8u\!"*7&7%$"+e*o^)G!"*$"+t)Gz&>!"*$"+Dy8u\!"*7%$"+e*o^G"!"*$"+t)GzN%!"*$"+Dy8u")!"*7%$"+V,?(H"!"*$"+oTu@W!"*$"+Y>HK")!"*7%$"+V,?(*G!"*$"+oTu@?!"*$"+Y>HK\!"*7&7%$"+V,?(*G!"*$"+oTu@?!"*$"+Y>HK\!"*7%$"+V,?(H"!"*$"+oTu@W!"*$"+Y>HK")!"*7%$"+!Q(\[8!"*$"+IRDxW!"*$"+U#3j6)!"*7%$"+!Q(\[H!"*$"+IRDx?!"*$"+U#3j"\!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7%7%$"+:;>N7!"*$"+xD@ZY!"*$"+vj=Kz!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+tRHi9!"*$"+9qTIZ!"*$"+EUL$)z!"*7%7%$"+tRHi9!"*$"+9qTIZ!"*$"+EUL$)z!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+]@gl;!"*$"+#Q8uo%!"*$"+R5C<")!"*7%7%$"+]@gl;!"*$"+#Q8uo%!"*$"+R5C<")!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+L$fuw"!"*$"+2wiMX!"*$"+h*eFG)!"*7%7%$"+L$fuw"!"*$"+2wiMX!"*$"+h*eFG)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+T&f*G<!"*$"+i'=/L%!"*$"+udm;%)!"*7%7%$"+T&f*G<!"*$"+i'=/L%!"*$"+udm;%)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+&Q3[c"!"*$"+Buy_T!"*$"+DO"yY)!"*7%7%$"+&Q3[c"!"*$"+Buy_T!"*$"+DO"yY)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+FgqP8!"*$"+')HepS!"*$"+udm;%)!"*7%7%$"+FgqP8!"*$"+')HepS!"*$"+udm;%)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+]yRM6!"*$"+=me7T!"*$"+h*eFG)!"*7%7%$"+]yRM6!"*$"+=me7T!"*$"+h*eFG)!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+n1aK5!"*$"+$Rs`E%!"*$"+R5C<")!"*7%7%$"+n1aK5!"*$"+$Rs`E%!"*$"+R5C<")!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+f//r5!"*$"+Q8epW!"*$"+EUL$)z!"*7%7%$"+f//r5!"*$"+Q8epW!"*$"+EUL$)z!"*7%$"+++++5!"*$"+++++]!"*$"+++++!*!"*7%$"+:;>N7!"*$"+xD@ZY!"*$"+vj=Kz!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+:;>N7!"*$"+xD@ZY!"*$"+vj=Kz!"*7%$"+tRHi9!"*$"+9qTIZ!"*$"+EUL$)z!"*7%$"+]@gl;!"*$"+#Q8uo%!"*$"+R5C<")!"*7%$"+L$fuw"!"*$"+2wiMX!"*$"+h*eFG)!"*7%$"+T&f*G<!"*$"+i'=/L%!"*$"+udm;%)!"*7%$"+&Q3[c"!"*$"+Buy_T!"*$"+DO"yY)!"*7%$"+FgqP8!"*$"+')HepS!"*$"+udm;%)!"*7%$"+]yRM6!"*$"+=me7T!"*$"+h*eFG)!"*7%$"+n1aK5!"*$"+$Rs`E%!"*$"+R5C<")!"*7%$"+f//r5!"*$"+Q8epW!"*$"+EUL$)z!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+!Q(\[H!"*$"+IRDx?!"*$"+U#3j"\!"*7%$"+moY>I!"*$"+<`D.@!"*$"+Y>HK\!"*7%$"+s1+$3$!"*$"+#o;)*3#!"*$"+Dy8u\!"*7%$"+U5$[6$!"*$"+F62U?!"*$"+v@'e-&!"*7%$"+d)*z-J!"*$"+KeDy>!"*$"+a!3x1&!"*7%$"+?E]^I!"*$"+qguA>!"*$"+e<p$3&!"*7%$"+MJ`!)H!"*$"+$oWn*=!"*$"+a!3x1&!"*7%$"+G$**p"H!"*$"+=L=5>!"*$"+v@'e-&!"*7%$"+e*o^)G!"*$"+t)Gz&>!"*$"+Dy8u\!"*7%$"+V,?(*G!"*$"+oTu@?!"*$"+Y>HK\!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7&7%$"+k*o*[H!"*$"+k*o*[>!"*$"+Fz$z*[!"*7%$"+k*o*[P!"*$"+k*o*[F!"*$"+Gz$z4%!"*7%$"+#Ro1"Q!"*$"+e;w1F!"*$"+\+V<T!"*7%$"+#Ro1,$!"*$"+d;w1>!"*$"+\+V<\!"*7&7%$"+#Ro1,$!"*$"+d;w1>!"*$"+\+V<\!"*7%$"+#Ro1"Q!"*$"+e;w1F!"*$"+\+V<T!"*7%$"+dGHoQ!"*$"+H#o,q#!"*$"+'3h%oT!"*7%$"+dGHoI!"*$"+H#o,!>!"*$"+&3h%o\!"*7&7%$"+dGHoI!"*$"+H#o,!>!"*$"+&3h%o\!"*7%$"+dGHoQ!"*$"+H#o,q#!"*$"+'3h%oT!"*7%$"+s<$)**Q!"*$"+WrqJF!"*$"+;*Q:B%!"*7%$"+r<$)*4$!"*$"+VrqJ>!"*$"+:*Q:.&!"*7&7%$"+r<$)*4$!"*$"+VrqJ>!"*$"+:*Q:.&!"*7%$"+s<$)**Q!"*$"+WrqJF!"*$"+;*Q:B%!"*7%$"+V$QK*Q!"*$"+4;L*y#!"*$"+_*pDG%!"*7%$"+V$QK4$!"*$"+3;L*)>!"*$"+^*pD3&!"*7&7%$"+V$QK4$!"*$"+3;L*)>!"*$"+^*pD3&!"*7%$"+V$QK*Q!"*$"+4;L*y#!"*$"+_*pDG%!"*7%$"+P5.^Q!"*$"+P5.^G!"*$"+t?1-V!"*7%$"+O5.^I!"*$"+O5.^?!"*$"+t?1-^!"*7&7%$"+O5.^I!"*$"+O5.^?!"*$"+t?1-^!"*7%$"+P5.^Q!"*$"+P5.^G!"*$"+t?1-V!"*7%$"+4;L*y$!"*$"+V$QK*G!"*$"+_*pDG%!"*7%$"+3;L*)H!"*$"+V$QK4#!"*$"+^*pD3&!"*7&7%$"+3;L*)H!"*$"+V$QK4#!"*$"+^*pD3&!"*7%$"+4;L*y$!"*$"+V$QK*G!"*$"+_*pDG%!"*7%$"+WrqJP!"*$"+s<$)**G!"*$"+;*Q:B%!"*7%$"+VrqJH!"*$"+r<$)*4#!"*$"+:*Q:.&!"*7&7%$"+VrqJH!"*$"+r<$)*4#!"*$"+:*Q:.&!"*7%$"+WrqJP!"*$"+s<$)**G!"*$"+;*Q:B%!"*7%$"+H#o,q$!"*$"+dGHoG!"*$"+'3h%oT!"*7%$"+H#o,!H!"*$"+dGHo?!"*$"+&3h%o\!"*7&7%$"+H#o,!H!"*$"+dGHo?!"*$"+&3h%o\!"*7%$"+H#o,q$!"*$"+dGHoG!"*$"+'3h%oT!"*7%$"+e;w1P!"*$"+#Ro1"G!"*$"+\+V<T!"*7%$"+d;w1H!"*$"+#Ro1,#!"*$"+\+V<\!"*7&7%$"+d;w1H!"*$"+#Ro1,#!"*$"+\+V<\!"*7%$"+e;w1P!"*$"+#Ro1"G!"*$"+\+V<T!"*7%$"+k*o*[P!"*$"+k*o*[F!"*$"+Gz$z4%!"*7%$"+k*o*[H!"*$"+k*o*[>!"*$"+Fz$z*[!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6.7%7%$"+%o+nj$!"*$"+%o+nj#!"*$"+o8StQ!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+a)QT$Q!"*$"+.tj,D!"*$"+dhxNR!"*7%7%$"+a)QT$Q!"*$"+.tj,D!"*$"+dhxNR!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+Tr`=S!"*$"+K$Q0[#!"*$"+ta2*4%!"*7%7%$"+Tr`=S!"*$"+K$Q0[#!"*$"+ta2*4%!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+p;Y>T!"*$"+fGY"e#!"*$"+GX#4I%!"*7%7%$"+p;Y>T!"*$"+fGY"e#!"*$"+GX#4I%!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+(pi$)4%!"*$"+Z6'ew#!"*$"+XQAkW!"*7%7%$"+(pi$)4%!"*$"+Z6'ew#!"*$"+XQAkW!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+;$*HjR!"*$"+;$*HjH!"*$"+L')fEX!"*7%7%$"+;$*HjR!"*$"+;$*HjH!"*$"+L')fEX!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+Z6'ew$!"*$"+(pi$)4$!"*$"+XQAkW!"*7%7%$"+Z6'ew$!"*$"+(pi$)4$!"*$"+XQAkW!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+fGY"e$!"*$"+p;Y>J!"*$"+GX#4I%!"*7%7%$"+fGY"e$!"*$"+p;Y>J!"*$"+GX#4I%!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+K$Q0[$!"*$"+Tr`=I!"*$"+ta2*4%!"*7%7%$"+K$Q0[$!"*$"+Tr`=I!"*$"+ta2*4%!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+.tj,N!"*$"+a)QT$G!"*$"+dhxNR!"*7%7%$"+.tj,N!"*$"+a)QT$G!"*$"+dhxNR!"*7%$"+,+++S!"*$"+,+++I!"*$"+++++S!"*7%$"+%o+nj$!"*$"+%o+nj#!"*$"+o8StQ!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+%o+nj$!"*$"+%o+nj#!"*$"+o8StQ!"*7%$"+a)QT$Q!"*$"+.tj,D!"*$"+dhxNR!"*7%$"+Tr`=S!"*$"+K$Q0[#!"*$"+ta2*4%!"*7%$"+p;Y>T!"*$"+fGY"e#!"*$"+GX#4I%!"*7%$"+(pi$)4%!"*$"+Z6'ew#!"*$"+XQAkW!"*7%$"+;$*HjR!"*$"+;$*HjH!"*$"+L')fEX!"*7%$"+Z6'ew$!"*$"+(pi$)4$!"*$"+XQAkW!"*7%$"+fGY"e$!"*$"+p;Y>J!"*$"+GX#4I%!"*7%$"+K$Q0[$!"*$"+Tr`=I!"*$"+ta2*4%!"*7%$"+.tj,N!"*$"+a)QT$G!"*$"+dhxNR!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I)POLYGONSG6$%*protectedGI(_syslibG6"6%7,7%$"+k*o*[H!"*$"+k*o*[>!"*$"+Fz$z*[!"*7%$"+#Ro1,$!"*$"+d;w1>!"*$"+\+V<\!"*7%$"+dGHoI!"*$"+H#o,!>!"*$"+&3h%o\!"*7%$"+r<$)*4$!"*$"+VrqJ>!"*$"+:*Q:.&!"*7%$"+V$QK4$!"*$"+3;L*)>!"*$"+^*pD3&!"*7%$"+O5.^I!"*$"+O5.^?!"*$"+t?1-^!"*7%$"+3;L*)H!"*$"+V$QK4#!"*$"+^*pD3&!"*7%$"+VrqJH!"*$"+r<$)*4#!"*$"+:*Q:.&!"*7%$"+H#o,!H!"*$"+dGHo?!"*$"+&3h%o\!"*7%$"+d;w1H!"*$"+#Ro1,#!"*$"+\+V<\!"*-I&STYLEG6$%*protectedGI(_syslibG6"6#I,PATCHNOGRIDG6$%*protectedGI(_syslibG6"-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"""!""!""!-I%MESHG6$%*protectedGI(_syslibG6"6#X.I)anythingG%*protectedG6"6"[gl'!%"!!$^`r":":"$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'POINTSG6$%*protectedGI(_syslibG6"6%7%$""$""!$""#""!$""&""!-I'COLOURG6$%*protectedGI(_syslibG6"6&I$RGBG6$%*protectedGI(_syslibG6"$"*++++"!")$""!""!$""!""!-I'SYMBOLG6$%*protectedGI(_syslibG6"6#I'CIRCLEG6$%*protectedGI(_syslibG6"-I*AXESSTYLEG6$%*protectedGI(_syslibG6"6#I$BOXG6$%*protectedGI(_syslibG6"-I(SCALINGG6"6#I,CONSTRAINEDG6$%*protectedGI(_syslibG6"

4. Plot the graph of a plane with tangent vectors <-5,1,6> and <3,1,-1> that passes through the point (0,4,-5). Show the vectors in your plot. 5. Plot the graph of a plane that passes through the points (0,1,2), (4,-1,1), and (-3,0,2). On your plot, show two vectors in the plane that share a base point AND show another vector IN the plane. The simplest expression that defines a plane is Ax + By + Cz = D, but the easiest to work with when juggling lines and planes is <n1,n2,n3> . (<x,y,z> - <p1,p2,p3>)=0. This is the form we use in the following code. Here, <n1,n2,n3> is a vector normal to the plane and (p1,p2,p3) is a point in the plane. 6. Explain why any vector <x,y,z> that satisfies the vector equation <n1,n2,n3> . (<x,y,z> - <p1,p2,p3>)=0 must be the position vector for a point in the plane with normal vector <n1,n2,n3> that passes through the point (p1,p2,p3). v3:=<n1,n2,n3>: v4:=<p1,p2,p3>: n1:=3: n2:=-1: n3:=1: p1:=5: p2:=-7: p3:=2: v5:=<-n2,n1,0>: v6:=CrossProduct(v3,v5): plane2:=plot3d([v4[1]+s*v5[1]+t*v6[1],v4[2]+s*v5[2]+t*v6[2],v4[3]+s*v5[3]+t*v6[3]], s=-5..5,t=-5..5, transparency=.5, color=blue, style=patchnogrid): vect2:=arrow(v4,v3,width = 0.4, head_width=1.5, color = black): point2:=pointplot3d(v4,color=red,symbol=circle): display([plane2,vect2,point2],axes=boxed,scaling=CONSTRAINED);

6*-I%MESHG6$%*protectedGI(_syslibG6"6&X.I)anythingG%*protectedG6"6"[gl'!%"!!$^`r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