Zero Vector:
A zero vector is a vector whose initial and terminal points coincide. It is denoted by 0 or 0̂. It has a magnitude of zero and does not have any direction.

Explanation:
When we talk about vectors, we usually think of them as directed line segments with an initial and terminal point. However, there is a special case where the initial and terminal points of a vector coincide, resulting in a zero vector.

Initial and Terminal Points Coincide:
When the initial and terminal points of a vector coincide, it means that the vector has no length or magnitude. It is essentially a point in space, representing a position but not a direction or displacement.

Properties of Zero Vector:
- Magnitude: The magnitude of a zero vector is zero. This means that the length of the vector is zero.
- Direction: A zero vector has no direction since it does not extend from one point to another.
- Addition: When a zero vector is added to any other vector, the result is the other vector itself. This is because adding zero does not change the value of a vector.
- Scalar Multiplication: When a zero vector is multiplied by any scalar, the result is still the zero vector. This is because multiplying zero by any number results in zero.

Examples:
- Consider a vector represented by a line segment from point A to point A. This vector has no length and no direction, and therefore it is a zero vector.
- If we have a vector with initial point (3, 4) and terminal point (3, 4), the vector is a zero vector since the points coincide.

Conclusion:
A vector whose initial and terminal points coincide is called a zero vector. It has a magnitude of zero and does not have any direction. The zero vector is a special case in vector algebra and has unique properties when it comes to addition and scalar multiplication.