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Prove that abcabc[a¯ b¯+c¯ a¯+b¯+c¯]=0 - Mathematics and Statistics

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Question

Prove that `[bar"a"  bar"b" + bar"c"  bar"a" + bar"b" + bar"c"] = 0`

Sum
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Solution

`[bar"a"  bar"b" + bar"c"  bar"a" + bar"b" + bar"c"]`

`= bar"a" * [(bar"b" + bar"c") xx (bar"a" + bar"b" + bar"c")]`

`= bar"a" * (bar"b" xx bar"a" + bar"b" xx bar"b" + bar"b" xx bar"c" + bar"c" xx bar"a" + bar"c" xx bar"b" + bar"c" xx bar"c")`

`= bar"a" * (bar"b" xx bar"a") + bar"a" * (bar"b" xx bar"b") + bar"a" * (bar"b" xx bar"c") + bar"a" * (bar"c" xx bar"a") + bar"a" * (bar"c" xx bar"b") + bar"a" * (bar"c" xx bar"c")`

`= 0 + 0 + bar"a" * (bar"b" xx bar"c") + 0 - bar"a" * (bar"b" xx bar"c") + 0`

= 0

shaalaa.com
Vector Triple Product
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Chapter 5: Vectors - Exercise 5.5 [Page 184]
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