Question

SHow that a.[(b+c)x(a+b+c)]=0

Answer 1

Answer:

a.[(b+c)×(a+b+c)]=0

Step-by-step explanation:

As we know for any vectors A,B and C

(A×B)= -(B×A) and A×(B+C)= (A×B)+(A×C)

So taking LHS of given question,

A×(B+C)+B×(C+A)+C×(A+B)

= (A×B)+(A×C)+(B×C)+(B×A)+(C×A)+(C×B)

= (A×B)+(A×C)+(B×C)-(A×B)-(A×C)-(B×C)

=0(proved)

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