A Simple Note on General Vectors

There are roughly two types of physical quantities: scalar and vector. A scalar quantity has only magnitude. However, a vector has both magnitude and direction. 

Vectors can be added using methods like the triangle method, parallelogram method, or component method. These methods help summarize the results of addition. 

This blog is about the resolution of vectors, their definition, important terms, revolving components into rectangular components, triangle law of vector addition and parallelogram law of vector addition, resolving vectors along with X and Y-Axis, and unit vectors across the coordinate axis.

General Vectors

The vector is the quantity that combines the duo – magnitude and direction. Vectors are depicted by the direct pointed line in which the length shows the vector and magnitude, and the orientation shows the direction of the vector. They have initial points and final points and are represented by arrows. 

Types of vectors

There are numerous types in which we can find and describe the vector. Each of them is unique, though easy to understand. They have specific properties to describe them. 

The zero vector is another sort of vector in which the value of the vector is zero, and also the origin and endpoint points of the vector are the same. The zero vector has no constituents and will not point in any direction.

Unit Vector

Among the different kinds of vectors, the Unit vector, as the name ‘unit’ suggests, is a vector with a magnitude equal to 1. It is also known as the multiplicative identity of vectors. The length of these vectors is 1. We also consider that any two unit vectors should not be called equal as they can have the same magnitude, but the direction in which the vectors are taken might differ. The main purpose of a unit vector is to indicate direction.

Position Vector

These vectors are used to determine the vectors’ position and direction of movement in a three-dimensional space. Here, the origin point is taken as 0, and there is one arbitrary point named P in the space. The vector OP-> is known as the position vector having the reference origin 0. The vector mainly denotes the location or position of the point.

Co-initial Vector

Co-initial vectors have a common origin point, and may scatter in different directions. For example, AB and AC are co-initial vectors since they have the same beginning point, ‘A.’ They are also called concurrent vectors.

Like Vector and Unlike Vector

Vectors having the same direction are called Like vectors. Alternatively, unlike vectors have the opposite direction concerning each other. 

Co-Planar Vector

Co-Planar vectors are three or more vectors that lie in the same plane or are parallel to the same plane. Sometimes, there is the possibility of finding any two vectors lying in the same plane. The scalar triple multiplication for the three vectors always equals zero, and they are always linearly dependent vectors. 

Collinear Vector

It is the type of vector in which two or more vectors are parallel to each other, disregarding the magnitude or direction. They never intersect with each other. For instance, if the vector ‘P’ is in the ‘A’-direction, and ‘Q’ is also in the same direction, they are collinear vectors. Their coordinates are the same. Another name for collinear vectors is Parallel vectors. 

Equal Vector

Equal Vectors have similar corresponding components. They own the same magnitude and direction, and their initial and terminal points might differ, but the length and direction must be identical.

Displacement Vector

When one vector is displaced from its place, it is known as the displacement vector. 

For instance, if some object is present at point ‘P’ at time =0 and afterward it is at point ‘R’ at time =t. The displacement can be determined as the vector distance between the starting point of the object and the ending point.

Negative Vector

A type of vector in which the two vectors have equal magnitude but opposite directions are called negative vectors. If we take two negative vectors, ‘P’ and ‘R,’ it can be represented as P = -R. 

Conclusion

We saw here that there are different types of vectors — the physical quantity, with the magnitude and direction. They are mathematical concepts, and there are different types of vectors, as discussed above. Vectors represent displacement, velocity, and acceleration, and help define the force applied on a body simultaneously in the three dimensions.