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{SECT 0 {PARA 3 "" 0 "" {TEXT -1 33 "Vector Functions and Space Curves
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "restart; interface(warnl
evel=0): with(plots): setoptions3d(scaling=constrained):" }}}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 7 "Example" }}{PARA 0 "" 0 "" {TEXT -1 15 "Pl
ot the curve " }{XPPEDIT 18 0 "r(t) = `<,>`(t,t^2,2*t);" "6#/-%\"rG6#%
\"tG-%$<,>G6%F'*$F'\"\"#*&F,\"\"\"%\"tGF." }{TEXT -1 1 "." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "spacecurve([t,t^2,2*t],t=-2..2,axes
=normal);" }}}{PARA 0 "" 0 "" {TEXT -1 53 "The curve is the intersecti
on of the parabolic sheet " }{XPPEDIT 18 0 "y = x^2;" "6#/%\"yG*$%\"xG
\"\"#" }{TEXT -1 15 " and the plane " }{XPPEDIT 18 0 "z = 2*x;" "6#/%
\"zG*&\"\"#\"\"\"%\"xGF'" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "s1 := plot3d([u,u^2,v],u=-2..2,v=-4..4):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "s2 := plot3d([u,v,2*u],u=-2..2,v=-2
..4,color=cyan,grid=[2,2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "display3d(s1,s2,axes=normal);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 
-1 7 "Example" }}{PARA 0 "" 0 "" {TEXT -1 15 "Plot the curve " }
{XPPEDIT 18 0 "r(t) = `<,>`(sin(t),sin(t), sqrt(2)*cos(t));" "6#/-%\"r
G6#%\"tG-%$<,>G6%-%$sinG6#F'-F,6#F'*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#F'F
5" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "spacecu
rve([sin(t),sin(t),sqrt(2)*cos(t)],t=0..2*Pi, axes=boxed, orientation=
[75,70]);" }}}{PARA 0 "" 0 "" {TEXT -1 43 "The curve is the interectio
n of the sphere " }{XPPEDIT 18 0 "x^2+y^2+z^2 = 2;" "6#/,(*$%\"xG\"\"#
\"\"\"*$%\"yGF'F(*$%\"zGF'F(F'" }{TEXT -1 24 " and the vertical plane \+
" }{XPPEDIT 18 0 "y = x;" "6#/%\"yG%\"xG" }{TEXT -1 1 "." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "s1 := plot3d(sqrt(2),t=0..2*Pi,p=0.
.Pi,coords=spherical):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "s
2 := plot3d([u,u,v],u=-1..1,v=-sqrt(2)..sqrt(2),color=cyan,grid=[2,2])
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "display3d(s1,s2, axes=
boxed, orientation=[75,70]);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "
Example" }}{PARA 0 "" 0 "" {TEXT -1 40 "Sketch the intersection of the
 cylinder " }{XPPEDIT 18 0 "x^2+y^2 = 4;" "6#/,&*$%\"xG\"\"#\"\"\"*$%
\"yGF'F(\"\"%" }{TEXT -1 25 " and the parabolic sheet " }{XPPEDIT 18 
0 "z = x^2;" "6#/%\"zG*$%\"xG\"\"#" }{TEXT -1 47 ". Find the parametri
c equations for this curve." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
58 "s1 := plot3d([2*cos(t),2*sin(t),v], t=0..2*Pi, v=-2..4.5):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "s2 := plot3d([u,v,u^2], u=-2
.5..2.5, v=-2.5..2.5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "d
isplay3d(s1, s2, axes=boxed);" }}}{PARA 0 "" 0 "" {TEXT -1 63 "Paramet
ric equations for te curve of intersection are given by " }{XPPEDIT 
18 0 "x = 2*cos(t);" "6#/%\"xG*&\"\"#\"\"\"-%$cosG6#%\"tGF'" }{TEXT 
-1 2 ", " }{XPPEDIT 18 0 "y = 2*sin(t);" "6#/%\"yG*&\"\"#\"\"\"-%$sinG
6#%\"tGF'" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "z = 4*cos(t)^2;" "6#/%
\"zG*&\"\"%\"\"\"*$-%$cosG6#%\"tG\"\"#F'" }{TEXT -1 1 "." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "spacecurve([2*cos(t),2*sin(t),4*cos
(t)^2], t=0..2*Pi, axes=normal);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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