{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 302 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 307 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 16 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE " Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 128 1 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE " " -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 20 0 0 0 0 0 1 2 0 0 2 0 0 0 1 }3 1 0 -1 5 3 0 0 0 0 0 0 18 0 }{PSTYLE "" 5 256 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 18 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 265 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 18 266 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 18 267 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 18 268 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 18 "" 0 "" {TEXT -1 14 "Maple Basics " }}{PARA 18 "" 0 "" {TEXT -1 8 "Lesson 1" }}{PARA 18 "" 0 "" {TEXT -1 7 "Vectors" }} {PARA 266 "" 0 "" {TEXT -1 37 "*revised from a Maple worksheet from " }}{PARA 268 "" 0 "" {TEXT -1 25 "Department of Mathematics" }}{PARA 267 "" 0 "" {TEXT -1 31 "N.C. State University 1999-2000" }}{PARA 257 "" 0 "" {TEXT 302 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Introduc tion" }}{PARA 0 "" 0 "" {TEXT -1 130 "Vector calculations using Maple \+ V are simple. This lesson introduces the basic Maple V commands neede d to do vector calculations." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 " Discussion" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Preliminaries" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "Defining Ve ctors" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "vector" {MPLTEXT 1 0 13 "A := [1,2,3];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "B := [5,0,5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "C := [x ,y,z];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "B;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " subs(\{x=1,y=2,z=3\},C);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "C;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 15 "Vector Addition" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A+B;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "A+B-C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 269 10 "Solution: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "vec(PQ):=[11,-5,0]-[1,4 ,-6];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Scalar multiplication" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "(1/10)*A;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "[1,2,3]*(1/10 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3*C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "Pi*B;" }}}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Length of a Vector" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm(A,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm(B,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm(C,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "norm(5*A, 2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "norm(5*C,2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "Solution:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "vec(RS):=[7,0,-9]-[2,-1,16];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "length_vec(RS):=norm(vec(RS),2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Inner (Dot ) and Cross Products" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "d otprod" {MPLTEXT 1 0 15 "innerprod(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "innerprod(B,A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "innerprod([5,0,5],[1,2,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "innerprod(A,C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "crossprod" {MPLTEXT 1 0 15 "crossprod(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "cros sprod(B,A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "crossprod([1 ,2,3],[5,0,5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "crossprod(A,C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Solution" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "vec(pq):=[4,5,6]-[1,2,3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "vec(pr):=[-2,7,11]-[1,2,3];" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "orthogonal_vector:=crossprod(vec(pq),vec(pr));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "Angle between Two Vecto rs" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "angle([1,0,0],[0,0,1]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "angle([1,0,0],[1,0,0]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "angle(A,A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Examples" }}{SECT 1 {PARA 0 "" 0 "" {TEXT 307 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 156 " From our textbook we know the method of doing this. We divide vector A by its length. That is , we multiply vector A by the reciprocal of the length of A." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "A:=[1,2,3];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "U := (1/norm(A,2))*A ;" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm(U,2);" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 262 "" 0 "" {TEXT -1 9 "Solution:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "F := [-1,1,3]; G := [2,4,3];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " Fparallel := (innerprod(F,G)/innerprod(G,G))*G;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Fperp := F-Fparallel;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "innerprod(G,Fperp);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "crossprod(G,Fparallel);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 263 "" 0 "" {TEXT -1 9 "Solution:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "U := [1,-1,3]-[1,0,1] ; V := [3,0,-1]-[1,0,1];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "N := crossprod(U,V);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " 2*(x-1 )+4*(y-0)+2*(z-1)=0;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 264 "" 0 "" {TEXT -1 9 "Solution:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "AB:=[21 7,314,617]-[-122,317,615];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "AC:=[3117,-217,615]-[-122,317,615];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "AreaTri angle := norm(crossprod(AB,AC),2)/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%,10);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 265 "" 0 "" {TEXT -1 9 "Solution:" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "Area := abs(innerprod([1,2,3],crossprod([-1,0,1],[2,5 ,5])));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Summary" }}{PARA 0 "" 0 "" {TEXT -1 58 "These co mmands are contained in the Maple library package " }{TEXT 0 6 "linalg " }{TEXT -1 30 ". You must enter the command " }{TEXT 0 13 "with(lina lg):" }{TEXT -1 22 " in order to use them." }}{SECT 1 {PARA 4 "" 0 "" {TEXT 0 4 "norm" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "See also " }{HYPERLNK 17 "Maple's n orm" 2 "linalg,norm" "" }{TEXT -1 6 " help." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 0 9 "innerprod" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "See also " }{HYPERLNK 17 "Maple' s innerprod" 2 "innerprod" "" }{TEXT -1 6 " help." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 0 9 "crossprod" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 0 5 "angle" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "9" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }