From the property of vector product, we notice that \vec{C} must be perpendicular to the plane formed by vector \vec{A} and \vec{B} . Thus \vec{C} is perpendicular to both \vec{A} and \vec{B} and (\vec{A} + \vec{B}) vector also, must lie in the plane formed by vector \vec{A} and \vec{B} . Thus \vec{C} must be perpendicular to \(\left(\vec{A} + \vec{B}\right)\) also but the cross product \((\vec{A} \times \vec{B})\) gives a vector \vec{C} which can not be perpendicular to itself. Thus the last statement is wrong.