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Question
Show that `vec"a" xx (vec"b" + vec"c") + vec"b" xx (vec"c" + vec"a") + vec"c" xx (vec"a" + vec"b") = vec0`
Sum
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Solution
`vec"a" xx (vec"b" + vec"c") + vec"b" xx (vec"c" + vec"a") + vec"c" xx (vec"a" + vec"b")`
= `vec"a" xx vec"b" + vec"a" xx vec"c" + vec"b" xx vec"c" + vec"b" xx vec"a" + vec"c" xx vec"a" + vec"c" xx vec"b"`
= `vec"a" xx vec"b" - vec"c" xx vec"a" + vec"b" xx vec"c" - vec"a" xx vec"b" + vec"c" xx vec"a" - vec"b" xx vec"c"`
= `vec0`
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