I have spent a lot of time on this question and I just cannot figure it out. I have asked peers and no one knows how to do it.
Show that, for the normal vector n=⎣⎢⎡n1n2n3⎦⎥⎤, using the formula fn(x)=x−2(n⋅nx⋅n⋅n) leads to the matrix:
Fn=n12+n22+n321⎣⎢⎡−n12+n22+n32−2n2n1−2n3n1−2n1n2n12−n22+n32−2n3n2−2n1n3−2n2n3n12+n22−n32⎦⎥⎤
Show that, for the normal vector n=⎣⎢⎡n1n2n3⎦⎥⎤, using the formula fn(x)=x−2(n⋅nx⋅n⋅n) leads to the matrix:
Fn=n12+n22+n321⎣⎢⎡−n12+n22+n32−2n2n1−2n3n1−2n1n2n12−n22+n32−2n3n2−2n1n3−2n2n3n12+n22−n32⎦⎥⎤
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