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:
Solution:
Vnet = V1 + V2
⇒ Vnet = [10,0] + [−10,0] = [0,0].
Here, the net velocity vector is a zero vector, indicating that the ship, despite the forces acting on it, remains stationary. This example illustrates the cancellation effect of opposing vectors resulting in a zero vector.
Example 2: Suppose a particle is subjected to two forces F1 = [5,3] N and F2 = [−5, −3] N. The resultant force (Fresultant) acting on the particle can be determined as:
Solution:
Fresultant = F1 + F2
⇒ Fresultant = [5, 3] + [−5, −3] = [0,0]
In this case, the net force is a zero vector, signifying that the forces are in equilibrium, and the particle remains at rest.
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