If `vec(a)= vec(b) + vec( c)`, then write the value of `vec(a).(vec(b) xx vec(c ))`

If vec(a) .vec(b) = 0 , then write the value of vec(a) xx(vec(b) xx vec(c))

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .

It the vectors vec(a), vec(b) and vec(c) form the sides vec(BC), vec(CA) and vec(AB) respectively of a triangle ABC, then write the value of vec(a) xx vec(c) + vec(b) xx vec(c) .