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Prove that vec(a)xx(vec(b)+vec(c))+vec...

Prove that
`vec(a)xx(vec(b)+vec(c))+vec(b)xx(vec(c)+vec(a))+vec(c)xx(vec(a)+vec(b))=0`

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If vec(a).vec(b)xx vec(c )≠0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a).vec(a')+vec(b).vec(b')+vec(c ).vec(c')=3