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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 44 "Area, Volume, and Torque
 in Three Dimensions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 151 "The cell below illustrates how Maple can compute the d
ot product and cross product of two vectors and how it can compute the
 determinant of a matrix.  " }{TEXT 256 16 "Evaluate it now." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "w
ith(linalg):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A := [[1, 2, 3], [4
, 5, 6], [1, 2, 1]]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(A);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "x := [1, 2, 3]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y := [4, 5, \+
6]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "dotprod(x, y);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "crossprod(x, y);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 150 "You can \+
use Maple to perform some of the algebraic computations needed to veri
fy the theorems in this module.  The following cell shows one example.
  " }{TEXT 257 16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "x := [x1, x2, x3]:\ny := \+
[y1, y2, y3]:\n\nLeftSide  := dotprod(crossprod(x, y), crossprod(x, y)
):\nRightSide := dotprod(x, x) * dotprod(y, y) - dotprod(x, y)^2:\n\ns
implify(LeftSide - RightSide);" }}}}{MARK "0 0 0" 44 }{VIEWOPTS 1 1 0 
1 1 1803 }