What is the significance of the zero vector? When I was studying about vectors and their use in physics, I found something called zero vector. My physics textbook says it is  

A vector whose initial and terminal points coincide is called zero vector, it has zero magnitude but an arbitrary direction, i.e. it cannot be assigned a direction.

My question is What is the significance of this zero vector?
For example, If the force acting on a body has no magnitude then is there any meaning/significance to say that the force has a direction? It can also be said that a vector +zero vector = same vector, then what?? Zero vector has bring no change in the vector. I m totally confused regarding the role of this zero vector in mathematics/physics. Please help. 
Thanks 
 A: Perhaps consider that two forces of equal magnitude but opposite direction would have a resultant force of zero magnitude and indeterminate direction. That is, their vector sum would be the zero vector. If there were no zero vector, how else would one describe this situation?
A: One property of the zero vector is that it is known as the "additive identity". Just like multiplying a number by 1 is the multiplicative identity, multiplying any number by 1 gets the same number back, adding $\vec{0}$ gets the same vector back. That makes it a unique element in any vector space, and it is the one vector every vector space is required to have. In fact, the zero dimensional vector space consists of the set $\left\{\vec{0}\right\}$.
As for thinking about magnitude and direction, that requires a vector space to have another structure that allows you to calculate the length of a vector. That structure is called a metric. The general definition of a vector's direction is the unit vector that points in the same direction as the vector. In notation, a vector's direction is given by:
$$\hat{n} = \frac{\vec{v}}{|\vec{v}|}.$$ For the zero vector, you get $0/0$ for each component, and thus, no definable direction for the zero vector.
