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Please tell me how [a b r]c+[b c r]a+[c a r]b=[a b c]r

Please tell me how [a b r]c+[b c r]a+[c a r]b=[a b c]r

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Akshat
 
(a x b) x (r x c) = [a b c]r – [a b r]c                  …....(1)
 
(a x b) x (r x c) = [b c a]r – [b c r]a                 ….......(2)
 
(a x b) x (r x c) = [a b c]r – [a b r]c                ….......(3)
 
Adding above 3 equations
 we get RHS as
 = 3 [a b c]r – {[a b r]c + [b c r]a – [c a r]b}              …........(4)
 
again
(a x b) x (r x c) = [a b c]r – [a b r]c                ….........(5)
 
from (1) & (5)-
[a b c]r – [a b r]c = [a r c]b – [b r c]a
so
[a b c]r = [a b r]c + [c a r]b + [b c r]a
 from (4)
 
 [a b r]c+[b c r]a+[c a r]b=[a b c]r
 
Regards
Arun ()askIITians forum expert)

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