Show that `(vec(A) - vec(B)) xx (vec(A) +vec(B)) = 2(vec(A) xx vec(B))`

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

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

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

The value of (vec(A)+vec(B))xx(vec(A)-vec(B)) is

[(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

What is (vec(a)- vec(b)) xx (vec(a) + vec(b)) equal to ?

If (3 vec(a) - vec(b)) xx (vec(a) + 3 vec(b))= k vec(a) xx vec(b) , then what is the value of k?

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 ?

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)