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If vec(a), vec(b), vec(c ) are three vec...

If `vec(a), vec(b), vec(c )` are three vectors such that `vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a)`, prove that `vec(a), vec(b), vec(c )` are mutually at right angles and `|vec(b)|=1, |vec(c )|=|vec(a)|`.

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