# Question #d3574

Jul 8, 2016

I prefer to conclude that it has no direction.

#### Explanation:

We know that a null vector is a vector having magnitude equal to zero. It is represented by $\vec{\text{O}}$.

1. It has no direction.

2. It may have any direction of your choice if being considered independently.

3. Since dot product of null vector with any other vector $\vec{V}$ is
$\vec{\text{O}} \cdot \vec{V} \equiv 0$,
therefore null vector is orthogonal to every vector in the corresponding Euclidean space.

4. We identify the direction of a vector with the unit vector we get after dividing it by its length. Since length (magnitude) of null vector is zero, and division by zero is indeterminate, hence it has no direction.

5. Assigning direction to a null vector is akin to assigning direction to a point.

As such it would be safe to conclude that it has no direction.