Given `vec(A)xxvec(B)=vec(0)` and `vec(B)xxvec(C )=vec(0)` Prove that `vec(A)xxvec(C )=vec(0)`

If vec(A) vec(B), vec(C ) are three vectors and one of them has zero magnitude , then given that vec(A) xx vec(B) = 0 and vec(B) xx vec(C ) = 0 , Prove that vec(A) xx vec(c ) = 0

If vec(a).vec(b)=0 and vec(a) xx vec(b)=0, " prove that " vec(a)= vec(0) or vec(b)=vec(0) .

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

Given that vec(A) xx vec(B) = 0 , vec(B) xx vec(C ) = 0 , find the value of vec(A) xx vec(C ) " if " vec (A) != 0 , vec(B ) != 0 , vec(B) != 0 and vec(C ) != 0

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

If vec( a) , vec( b) , vec( c ) are non coplanar non-zero vectors such that vec( b) xxvec( c) = vec( a ), vec( a ) xx vec( b) =vec( c ) and vec( c ) xx vec( a ) = vec ( b ) , then which of the following is not true

Assertion: vec(PQ)xx(vec(RS)+vec(ST))!=0 , Reason : vec(PQ)xxvec(RS)=vec0 and vec(PQ)xxvec(ST)!=vec0 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

The angle between vec(A)+vec(B) and vec(A)xxvec(B) is

If vec(a)vec(b)vec(c ) and vec(d) are vectors such that vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c ) = vec(b)xxvec(d) . Then show that the vectors vec(a) -vec(d) and vec(b) -vec(c ) are parallel.

If vec(A)xxvec(B)=vec(B)xxvec(A) , then the angle between vec(A) and vec(B) is-