Properties of Vectors
Various properties that are useful in the study of vectors and that help us to solve various problems including the vector are,
- Dot product of two vectors is commutative, i.e. A . B = B. A
- Cross product of two vectors is not commutative, i.e. A × B ≠ B × A
- Dot product of two vectors represents a scalar quantity in the plane of two vectors
- Cross product of two vectors represents a vector quantity, perpendicular to the plane containing the two vectors.
- i . i = j . j = k . k = 1
- i . j = j . k = k . i = 0
- i × i = j × j = k × k = 0
- i × j = k; j × k = i; k × i = j
- j × i = -k; k × j = -i; i × k = -j
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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