prove that axbxc= a.(cb)-a.(b-c)
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Step-by-step explanation:
B×CB×C is a vector purpendicular to the plane formed by BB and CC. Hence the vector A×(B×C)A×(B×C) lies in the plane formed by BB and CC.
So we can write A×(B×C)A×(B×C) as,
A×(B×C)=A×(B×C)=αB−βCαB−βC ⋯†⋯†
Multiply(dot product) †† by AA to get,
A.(A×(B×C))=A.(A×(B×C))=α(A.B)−β(A.C)α(A.B)−β(A.C)
Since
A.(A×(B×C))=A.(A×(B×C))=(A×A).(B×C)=0(A×A).(B×C)=0
We get α(A.B)−β(A.C)=0α(A.B)−β(A.C)=0
α
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