- #1

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## Main Question or Discussion Point

If [itex]A\in O(3)[/itex] and [itex]v,w\in\mathbb{R}^3[/itex], then

[tex]

(Av)\times (Aw) = (\textrm{det}\;A) A(v\times w)

[/tex]

is right, right?

Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?

[tex]

(Av)\times (Aw) = (\textrm{det}\;A) A(v\times w)

[/tex]

is right, right?

Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?