1800-150-456-789
FlagBACK
Flag Vectors> if a b c be three non-coplanar vectors an...
question mark

if a b c be three non-coplanar vectors and r be any arbitrary vector then (a×b)×(r×c)+(b×c)×(r×a)+(c×a)×(r×b) is equal to (1)0 (2)[a b c]r (3)2[a b c]r (4)3[a b c]r

Akshat Agrawal , 7 Years ago
Grade 12
anser 2 Answers
Arun

Last Activity: 7 Years ago

Dear Akshat
 
we have
 
(a x b) x (r x c)
= ((a x b ) . c) r – ((a x b) . r) c
 = [a b c] r – [a b r] c
similarly
(b x c) x (r x a) = [b c a] r – [b c r] c
 
and 
(c x a) x (r x b) = [c a b] r – [c a r] b
 
when we add all three
 
we get
3 [a b c] r  –  [a b c] r = 2 [a b c] r
hence option 3 is correct
 
reagrds
Arun (askIITians forum expert)

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the solution to your problem.
 
we have,
(a x b) x (r x c)
= ((a x b ) . c) r – ((a x b) . r) c
 = [a b c] r – [a b r] c
similarly
(b x c) x (r x a) = [b c a] r – [b c r] c
and 
(c x a) x (r x b) = [c a b] r – [c a r] b
when we add all three
we get
3 [a b c] r  –  [a b c] r = 2 [a b c] r
hence option 3 is correct
 
Thanks and regards,
Kushagra

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on vectors

question mark
A body is rotating with an angular velocity of 2radians per second about the line joining (1, 2,3) and (2, 3,5) find the velocity of the particle of the body which is momentarily at (3, 5,6) 
 
vectors
0 Answer Available

Last Activity: 2 Years ago

question mark
Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQ
Vector
vectors
0 Answer Available

Last Activity: 3 Years ago

question mark
Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A
vectors
0 Answer Available

Last Activity: 3 Years ago

question mark
the mean of 30 observations was 17 with sd2. later it was found that two of the observations were incorrect, which were recorded as 19vand 21.find the correct sd if the incorrect values are deleted and correct values 22 and 15 are included
vectors
0 Answer Available

Last Activity: 3 Years ago

question mark
Find the component of 2i +3j +k in the direction of 3i-j 
 
vectors
1 Answer Available

Last Activity: 3 Years ago