Question

if a,b,c are three vectors such that a x b=c , b x c=a , c x a=b then prove that |a|=|b|=|c|

Answer 1

HOPE THIS IS HELPFUL
REFER TO THE PIC 
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Answer 2

=a×b=c

=b×c=a

=C×a=b

Let, 

=|a|=|b|= b and |c|=c

=a×b=c

=ab sinπ/2 c^=c^

=ab=c

=b×c=a

=bc sinπ/2 a^=aa^

=bc=a

=C×a=b

=Ca sinπ/2 b^=bb^

=Ca=b

From eq (1) ,(2)and(3)

We get a=b=c=1