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If ` vec u , vec v and vec w` are three non-coplanar vectors, then prove that `( vec u+ vec v- vec w) . [ [( vec u- vec v)xx( vec v- vec w)]]= vec u . vec v xx vec w`

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`(vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)=)(vecu+vecv-vecw).(vecuxxvecv-vecuxxvecw-vecvxxvecv+vecvxxvecw)`
`=(vecu+vecv-vecw).(vecuxxvecv-vecuxxvecw+vecvxxvecw)`
`= 0-0+vecu.(vecvxxvecw)+0-vecv.(vecuxxvecw)+0-vecw.(vecuxxvecv)+0-0`
`[vecu vecv vecw]+[vecv vecw vecu] - [vecwvecuvecv]=vecu.(vecvxxvecw)`
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