IIT JEE , AIEEE Forum - Mathematics , Vectors

karthik_abiram

Hii,

The answer is [a b c]r

here is the method............

consider (a x b) x (c x r )

Expanding through 2 possible wayz.........

#(a x b) x (c x r ) =[ a c r ] b - [c r b ]a

= - { [ c a r ] b + [b c r ] a }----------eq1

# (a x b) x (c x r ) = [ a b r ] c - [a b c ] r----------eq2

From eq1 and eq 2.............................

[ a b r ] c - [a b c ] r = - { [ c a r ] b + [b c r ] a }

[b,c,r]a + [c,a,r]b + [a,b,r]c = [a b c ] r-------------------------

so, the value of the given is [a b c ] r

cheers!