Question

What is means of zero vector? Explain with example?

Answer 1

Null vector is a vector with a zero magnitude. Vectors are the elements of vector space having magnitude and direction. Vector space is a set with binary operators and it does satisfy some rules using those operators. Vector space is a set of data or numbers which has two binary operators and some axioms which are satisfied using those operators. Additive inverse is one such property of a vector space which is satisfied using the null vector. Null vector is nothing but the identity element of vector space.
A vector with zero magnitude but the certain direction is known as a null vector.

If a→ is a vector than |a |=0|a→|=0. It means that the vector is pointing in a certain direction but is still there.
or The identity element of vector space is known as zero or null vector.

In a vector space, the additive inverse does exist. If there is a vector v, and a vector -v then there must exist a zero or null vector such that v + (-v) = 0.
A vector may have any number of dimensions. A null vector is one which has all the components as zero. For a two-dimensional vector, the zero vector is (0, 0) while for three-dimensional vector the zero vector is (0, 0, 0). It goes on like this for any number of dimensions.

The direction of a null vector is undefined. It can be any direction. The direction of a null vector will be like getting the direction of a point. It is undefined mostly but can be defined in complex spaces.
Here have been given some examples of a null vector.

1. Two people pulling a rope in opposite directions with equal force.

2. Displacement of throwing an object upward and then again holding it at the same position.

3. The velocity of a train standing still on a platform.

4. Acceleration of a car going at a uniform speed.