Prove that ,
` vec(a) xx ( vec (b) + vec(c)) + vec(b) xx (vec(c) + vec(a)) + vec(c)xx(vec (a) + vec(b)) = vec(0)`

Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a))

Prove that vec(a)xx(vec(b)+vec(c))+vec(b)xx(vec(c)+vec(a))+vec(c)xx(vec(a)+vec(b))=0

For any three vectors vec(A), vec(B) and vec(C) prove that vec(A) xx (vec(B) +vec(C)) +vec(B) xx (vec(C) +vec(A)) + vec(C) xx (vec(A) +vec(B)) = vec(O)

[(vec(a) xx vec(b)) xx (vec(b) xx vec(c)), (vec(b) xx vec(c)) xx (vec(c) xx vec(a)),(vec(c) xx vec(a)) xx (vec(a) xx vec(b))] is equal to

Prove that (vec(a)-vec(b)) xx (vec(a) +vec(b))=2(vec(a) xx vec(b))

Show that vec a xx (vec b xxvec c) + vec b xx (vec c xxvec b) + vec c xx (vec a xxvec b) = 0

Let vec(a), vec(b), vec(c) be three vectors mutually perpendicular to each other and have same magnitude. If a vector vec(r) satisfies vec(a) xx {(vec(r) - vec(b)) xx vec(a)} + vec(b) xx {(vec(r) - vec(c)) xx vec(b)} + vec(c) xx {(vec(r) - vec(a)) xx vec(c)} = vec(0) , then vec(r) is equal to :

The vectors vec(a), vec(b), vec(c ) and vec(d) are such that vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) xx vec(d) . Which of the following is/are correct? 1. (vec(a)- vec(d)) xx (vec(b) - vec(c ))= vec(0) 2. (vec(a) xx vec(b))xx (vec(c ) xx vec(d))= vec(0) Select the correct answer using the codes given below

[vec a xx (3vec b + 2vec c), vec b xx (vec c-2vec a), 2vec c xx (vec a-3vec b)]

The vectors vec a xx (vec b xxvec c), vec b xx (vec c xxvec a), vec c xx (vec a xxvec b) are