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)`

For any three vectors vec a, vec b & vec c prove that (vec b xxvec c) xx (vec c xxvec a) = [vec with bvec c] 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))=0

Let three vectors vec(a), vec(b) and vec(c ) be such that vec(a) xx vec(b) = vec(c), vec(b) xx vec(c) = vec(a) and |vec(a)| = 2 . Then which one of the following is not true ?

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 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

If vec(A)+vec(B)+vec(C )=0 then vec(A)xx vec(B) is

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 :

Prove that : {(vec(b)+vec(c ))xx(vec(c )+vec(a))}.(vec(a)+vec(b))=2[vec(a)vec(b)vec(c )]

Prove that : (vec(b)+vec(c )).{(vec(c )+vec(a))xx(vec(a)+vec(b))}=2 [vec(a)vec(b)vec(c )] .