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Question
If `bar"a", bar"b", bar"c"` are three non-coplanar vectors show that `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b") = 0`
Solution
LHS = `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b")`
`= [(bar"a" bar"b" bar"c")]/[(bar"c"bar"a"bar"b")] + [(bar"b" bar"a" bar"c")]/[(bar"c" bar"a" bar"b")]`
`= [(bar"a" bar"b" bar"c")]/[(bar"a" bar"b" bar"c")] - [(bar"a" bar"b" bar"c")]/[(bar"a" bar"b" bar"c")]`
= 0 = RHS.
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