Please tell me how [a b r]c+[b c r]a+[c a r]b=[a b c]r
Akshat Agrawal , 8 Years ago
Grade 12
Vectors> Please tell me how [a b r]c+[b c r]a+[c a...
1 Answers
Arun
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)
Approved Last Activity: 8 Years ago
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on vectors
Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQVector
Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQ
Vector
vectors
1 Answer Available
Last Activity: 4 Years ago
Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A
Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A
vectors
1 Answer Available
Last Activity: 4 Years ago
Find the component of 2i +3j +k in the direction of 3i-j
Find the component of 2i +3j +k in the direction of 3i-j
vectors
1 Answer Available
Last Activity: 4 Years ago