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geometry

 CrossProduct
 compute the cross product of two directed segments

 Calling Sequence CrossProduct(dseg1, dseg2)

Parameters

 dseg1, dseg2 - two directed segment

Description

 • The cross product $\mathrm{dseg1}X\mathrm{dseg2}$ can be interpret as the signed area of the parallelogram formed by the point $0,0$, dseg1, dseg2 and $\mathrm{dseg1}+\mathrm{dseg2}$.
 • Note that the tails of dseg1 and dseg2 must be the same.
 • The command with(geometry,CrossProduct) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,1,1\right),\mathrm{point}\left(C,11,5\right):$
 > $\mathrm{dsegment}\left(\mathrm{dseg1},A,B\right):$$\mathrm{dsegment}\left(\mathrm{dseg2},A,C\right):$
 > $\mathrm{CrossProduct}\left(\mathrm{dseg1},\mathrm{dseg2}\right)$
 ${-}{6}$ (1)
 > $\mathrm{triangle}\left(T,\left[A,B,C\right]\right)$
 ${T}$ (2)
 > $\mathrm{area}\left(T\right)$
 ${3}$ (3)

 See Also

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