Are you a mathematics junkie and love to find out about it in depth? Then our articles will suit you the best. Here, you will find articles on different topics from the world of mathematics. Since we aim to simplify the various complexities of mathematics.
Through our article, we pick a topic and explain it in an easily comprehensible way. As you might have read from the title that today we have picked up Vectors. It is one of the fundamental concepts in mathematics. If you want to revise the types and properties of vectors in-depth then you must go through the article thoroughly.
The Purpose & Properties Of Vectors
A vector carries point A to point B. The length between the two points is called the magnitude of the vector and the direction of the displacement between the two points is called the direction of the vector. Let’s find out more about the purpose and properties of vectors.
- Vectors are geometrical entities that consist of a magnitude and a direction. They are used to represent physical quantities that have both magnitude and direction such as acceleration, displacement, velocity, etc.
- It can be depicted with a line that has an arrow indicating its direction and its length indicating the magnitude in two or three dimensions. Hence, vectors are depicted by arrows, which have initial points and terminal points.
- The addition of vectors is commutative and associative.
- The dot product of two vectors is a scalar and lies in the plane of the two vectors.
- The cross product of two vectors is a vector, which is perpendicular to the plane containing these two vectors.
The Types Of Vectors
Vectors can be of various types based on their direction, magnitude, and their relationship with other vectors. Let’s look into the type of vectors one by one.
- Unit Vector – Vectors that have a magnitude equal to 1 are called unit vectors. These vectors are mostly used to indicate the direction.
- Zero Vector – The ones that have 0 magnitudes are called zero vectors. The zero vector has zero magnitudes and no direction. They are also called the additive identity of vectors.
- Equal Vector – When two or more vectors have their corresponding components equal they are called equal vectors. They carry the same magnitude as well as direction. They may have different initial and terminal points but the magnitude and direction would always be equal.
- Parallel Vector – When two or more vectors have the same direction but not always the same magnitude they are said to be parallel vectors. The angles of the direction of parallel vectors vary by zero degrees. The vectors whose angle of direction varies by 180 degrees are called antiparallel vectors and they are antiparallel opposite in directions.
- Position Vector – These types of vectors are meant to determine the position and direction of movement of the vectors in a 3-D setting. The magnitude and direction of position vectors can be changed relative to other bodies. These vectors are also known as the location vector.
- Negative Vector – A vector can be referred to as the negative of another vector if they have the same magnitudes opposite in directions. For example, if vectors A and B have identical magnitudes but opposite directions, then vector A will be called the negative of vector B or vice versa.
- Co-initial Vectors – When two vectors have the same initial point they are known as co-initial vectors.
- Orthogonal Vector – Two or more vectors in an area are said to be orthogonal if the angle between them is 90 degrees.