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Prove that ababab2(a¯-b¯)×2(a¯+b¯)=8(a¯×b¯) - Mathematics and Statistics

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Sum

Prove that `2(bar"a" - bar"b") xx 2(bar"a" + bar"b") = 8(bar"a" xx bar"b")`

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Solution

LHS = `2(bar"a" - bar"b") xx 2(bar"a" + bar"b")`

`= 4[(bar"a" - bar"b")xx(bar"a" + bar"b")]`

`= 4[bar"a" xx (bar"a" + bar"b") - bar"b" xx (bar"a" + bar"b")]`

`= 4 (bar"a" xx bar"a" + bar"a" xx bar"b" - bar"b" xx bar"a" - bar"b" - bar"b")`

`= 8 (bar"a" xx bar"b")`    ....`[∵ bar"a" xx bar"a" = bar"b" xx bar"b" = bar"0"  "and" - (bar"b" - bar"a") = bar"a" xx bar"b"]`

= RHS

∴ `2(bar"a" - bar"b")xx2(bar"a" + bar"b") = 8(bar"a" xx bar"b")`

Concept: Vector Product of Vectors (Cross)
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