What is a Unit Vector?
The unit vector of any given vector is the vector obtained by dividing the given vector by its magnitude. As the name suggests a unit vector is a vector whose magnitude is one(1). It is depicted by any English letter with an inverted V or cap on top of it. Unit vectors have a length of one. Unit vectors are commonly used to indicate a vector’s direction. The direction of a unit vector is the same as that of the provided vector, but its magnitude is one unit.
Unit Vector Definition
A unit vector is a vector with a magnitude of 1. It is used to specify a direction and has no other magnitude
We define a unit vector in each 3-D axis as,
- Unit vector in the x-direction is i
- Unit vector in the y-direction is j
- Unit vector in the z-direction is k
Also, the magnitude of this vector is,
- |i| = 1
- |j| = 1
- |k| = 1
The unit vector in the x, y, and z direction unit vectors are shown in the image below:
Before learning more about them let’s first learn about the magnitude of the vector.
Magnitude of Vector
The strength of any vector is given by the magnitude of the vector. Any vector has both magnitude and direction and the magnitude of the vector is calculated by taking the sum of the square of individual components of the vector and then taking its square root. For any [Tex]\vec{A} [/Tex] = ai + bj + ck the vector’s magnitude formula is,
[Tex]|\vec{A}|[/Tex]= √(a2 + b2 + c2)
We can understand this concept with the help of the example discussed below:
Example: Find the magnitude of vector [Tex]\vec{V}[/Tex] = 2i + 3k – j
Solution:
Given Vector,
[Tex]\vec{V} [/Tex] = 2i + 3k – j
Magnitude of vector is:
|V| = √(22 + 32 + (-1)2)
⇒ |V| = √(14) units
Unit Vector
Unit Vector: Vector quantities are physical quantities that have both magnitude and direction. We define them using their initial point and final point. Unit vectors are the vectors that have a magnitude of 1. For example [Tex]\vec A [/Tex] = 2i + 3j is not a unit vector as its magnitude is,
|A| = √(22 + 32) = √(13) ≠ 1
Unit vectors are the vectors that are used to give the direction of the vector. We can easily get the unit vector of the vector by simply dividing the vector by its magnitude.
In this article, we will learn about what is a unit vector, its formula, examples, and others in detail.
Table of Content
- What is a Unit Vector?
- Unit Vector Notation
- Unit Vector Formula
- How to Calculate the Unit Vector?
- Unit Vector Parallel to another Vector
- Unit Vector Perpendicular to another Vector
- Applications of Unit Vector
- Properties of Vectors
- Unit Vector Examples