" 14.Prove that "vec A*(A times B)=0

Prove that abs(vec(a) times vec(b))=(vec(a)*vec(b))tantheta , where theta is the angle between vec(a) and vec(b) .

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

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

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

Prove that (vec B timesvec c)*[vec A times(vec B timesvec C)]=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

For any to vectors vec A and vec B , prove that |vec A xx vec B|^2 = A^2 B^2 - ( vec A. vec B)^2 .

If vec α and vec β are any vectors, prove that vec β * (vec α xx vec β) =0 .

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)