If `vec A xx vec B= vec C xx vec B`, show that `vec C` need not be equal to vec A`.

If vec A xx vec B=vec A xx vec C , is it correct to conclude that vec B =vec C ?

If three vectors vec A, vec B and vec C are such that vec A .vec B =vec A .vec C , vec A xx vec B = vec A xx vec C , vec A!= vec 0 then prove that vec B =vec C .

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot\ vec b= vec adot\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

If vec(a) xx vec(b)= vec(c) xx vec(d) and vec(a) xx vec(c) =vec(b) xx vec(d)," show that " (vec(a)- vec(d)) " is parallel to " (vec(b)-vec(c)) , it being given that a !=d and b != c.

Fven that vec A xx vec B= vec B xx vec C = vec 0 . If vec A. vec B and vec C are not null vectors, find the value of vec Cxx vec A .

Let vec a xx vec b,vec b xx vec c,vec c xx vec a are non coplanar vectors and [[vec a,vec b,vec c]]=1.vec r is a vector such that vec r.vec a=vec r.vec b=vec r.vec c=2, then area of triangle whose vertices are vec a,vec b and vec c is (A) |vecr|/2 (2) 2|vecr| (C) |vecr|/4 (D) 4|vecr|

Let veca = hati - 2 hatj + 2hatk and vec b = 2 hati - hatj + hatk be two vectors. If vec c is a vector such that vecb xx vec c = vec b xx vec a and vec c vec a = 1 , then vec c vec b is equal to :

Let lambda = vec a xx (vec b + vec c), vec mu = vec b xx (vec c + vec a) and vec nu = vec c xx (vec a + vec b). Then

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to