Amplifications
You can easily change the translation vector v by using three new sliders. The translation is done before the rotations (moving it afterwards is less interesting).
Reflection in the plane
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Insert three sliders a, b, c to represent the plane Π. The variable names may be taken, in that case rename the points.
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Input the normal vector of the plane n.
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Show that the reflection matrix can be written as S=I-2n·nT, where I denotes the unit matrix. The transpose of a vector v is written
Transpose[v].
As opposed of a rotation, a reflection can either be ”on” or ”off”. To accomplish this you can insert a slider reflection taking on the values 0 or 1. Then let S=I-2n· reflection·nT
Try out GeoGebra by letting a=b=c=0!
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License
