Please tell me how [a b r]c+[b c r]a+[c a r]b=[a b c]r
Akshat Agrawal , 7 Years ago
Grade 12
Vectors> Please tell me how [a b r]c+[b c r]a+[c a...
1 Answers
Arun
Last Activity: 7 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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