Zero Vector (Null Vector)

Define Zero Vectors.

A zero vector, denoted as 0, is a special point in space where all components are precisely zero.

What is Null Vector?

A null vector, also known as a zero vector, is a vector with all its components equal to zero.

Do Two Null Vectors have Same Direction?

Since, the direction of null vector is undefined hence the direction of two null vectors can’t be decided whether they are same or not

How Do You Find the Zero Vectors?

To find the zero vector, we multiply the vector from a vector space with scalar 0.

What is Difference between Zero Vector and Zero Scalar?

Zero Vector has magnitude equal to zero value in vector space that is it still has direction but undefined while zero scalar has magnitude zero and no direction



Zero Vector

Zero Vectors are the vectors with all its components zero. A zero vector or a null vector is defined as a vector in space with a magnitude equal to 0 and an undefined direction. The zero-vector symbol for three-dimensional space is given by [Tex]\overrightarrow{\rm 0} [/Tex] = (0, 0, 0), and the zero-vector symbol for two-dimensional space is given by [Tex]\overrightarrow{\rm 0} [/Tex] = (0, 0).

In this article, we will learn about zero vectors with zero vector definition, zero vector symbol, properties of zero vectors, and, the significance of zero vectors.

Table of Content

  • What is Zero Vector (Null Vector)?
  • Zero Vector Explanation
  • Properties of Zero Vector (Null Vector)
  • Significance of Zero Vector (Null Vector)
  • Solved Examples

Similar Reads

What is Zero Vector (Null Vector)?

Zero Vectors, as the name suggests, are vectors characterized by a magnitude of zero. In the realm of vector algebra, these special vectors hold distinctive properties that set them apart from non-zero vectors. Understanding their nature is fundamental for various mathematical applications....

Zero Vector Example

Consider a scenario where two individuals are engaged in a tug-of-war, each pulling a rope with an equal force but in opposite directions. In this situation, the forces applied by the two individuals cancel each other out due to their opposing directions....

Zero Vector in Different Coordinate Systems

Zero vector is represented differently in different coordinate systems: Cartesian, polar, cylindrical, and spherical....

Properties of Zero Vector (Null Vector)

Zero Vectors exhibit unique properties that distinguish them from non-zero vectors. Understanding these properties is crucial for manipulating vectors in mathematical expressions. Some key properties include:...

Significance of Zero Vector (Null Vector)

Zero Vectors hold significance in various mathematical and scientific contexts. Their properties find applications in linear algebra, physics, computer science, and engineering. Understanding and leveraging these vectors enhance problem-solving capabilities and mathematical reasoning....

Zero Vector – Solved Examples

Example 1: Consider a ship moving eastward with a velocity vector V1 = [10,0] and /s, and a strong westward wind exerting a force represented by the vector V2 = [−10,0] m/s. The net velocity (Vnet) of the ship can be calculated as:...

Zero Vector – Practice Questions

Q1: Given a vector P = [3, −4] find the vector Q such that P+Q=0...

Zero Vector (Null Vector) – FAQs

Define Zero Vectors....