Final answer:
The zero vector, also known as the null vector, is represented by having all components equal to zero, such as <0,0> in two-dimensional space. It has no length and no direction and indicates a point at the origin of the coordinate system. The representation varies with the dimensionality of the vector space.
Step-by-step explanation:
The question pertains to the representation of a zero vector in vector algebra. A zero vector, which can also be referred to as a null vector, is a vector that has all its components equal to zero. For example, in two-dimensional space, it can be written as <0,0>. The zero vector has no length and no direction, which signifies that it represents a point at the origin of the coordinate system.
In physics, the concept of a zero vector may also apply in different contexts, such as describing the velocity of an object that is at rest. In such scenarios, various instances like a head-on collision where the incoming ball stops (v1 = 0), the absence of a collision where the incoming ball continues unaffected (v2 = 0), or a situation where the angle of separation is 90°, resulting in the cosine of the angle being zero, are examples where the term representing the vector can be zero.
It is essential to note that the ways a zero vector can be written out vary depending on the dimensions of the vector space. For instance, in three-dimensional space, the zero vector is typically written as <0, 0, 0>. As long as the magnitude is zero and the direction is undetermined or non-existent, the representation of a zero vector is valid irrespective of the dimensionality of the space.