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In physics, mathematical quantities are used to define the motion of objects. These mathematical quantities are of two types: vector quantities and scalar quantities, and we will discuss their representation and the product of those quantities. We will also come across terms such as distance, displacement, acceleration, speed, and velocity. The vector is a quantity that has both magnitude and direction. In diagrams, vectors are shown as a pointed line in which the length shows the vector and magnitude, and the orientation shows the direction of the vector. Velocity is a vector quantity.
Collinear Vectors
Collinear vectors are two or more vectors parallel to each other, disregarding the magnitude or direction. They never intersect with each other. For instance, if the vector P is in the direction A, and Q is also in the same direction, they are collinear vectors. The coordinates of P and Q are the same. Another name for collinear vectors is parallel vectors. The vectors should be parallel to the same line regardless of magnitude and direction. The collinear vectors should travel in the same line or parallel to each other in the same or opposite direction.
For example
- Parallel vectors can be scalar with another vector.
- In 3D, the cross product of a collinear vector is zero.
Types of vectors
Both scalars and vectors can represent the type of quality of any physical or mathematical object. There are ten types of vectors.
Co-initial vector
In co-initial vectors, the beginning points of two or more distinct vectors are the same. All vectors of this type begin from the same point. The vectors are called co-initial vectors because their origin points are the same.
Collinear vectors
The collinear vector is another vector in which two or more vectors, regardless of magnitude or direction, are parallel. Because they are parallel, they never cross paths.
Zero Vectors
The value of the zero vector is zero and the origin and the endpoint points of the vector are the same. The zero vector has no constituents and will not point in any direction.
Unit Vector
The unit vector is a subtype of a vector whose value is based on the length of one unit. Unit vectors are defined as any vectors with a magnitude of one.
Position Vector
A position vector is a vector in which the origin point is set to O, and one random point in the space is designated as A. The position vector with the reference origin O is known as vector AO.
Coplanar Vectors
Coplanar vectors have three or more vectors in the same plane or that can lie in a parallel plane. There is always the chance of finding two different vectors in the same plane, referred to as coplanar vectors.
Unlike and Like Vectors
Like vectors are the type of vectors that have the same direction. Unlike vectors are vectors that have the same magnitude but are in opposite directions.
Equal Vectors
Equal vectors are the vectors in which two or more vectors with the same magnitude and direction are considered equal.
Displacement Vector
The displacement vector is the sort of vector that occurs when one vector is shifted from its original position. The vector distance between the object’s starting and final points can determine the displacement.
Negative Vector
A negative vector is a form of vector in which the value of both vectors is equal, but the directions are opposite. We can write them as
a = -b. This is known as a negative vector.
Conclusion
A scalar quantity represents the magnitude of an object without direction. However, a quantity that has both magnitude and direction is a vector quantity. Thus, the fundamental distinction between scalar and vector values is direction; scalar quantities lack direction, but vector quantities have direction.
