Resolution of Vectors

Physical quantities can be divided into two categories, namely scalars and vectors. Quantities such as mass or density can only be defined by their numerical values ​​and corresponding units. These quantities are called “scalars”. However, quantities such as velocity or force need the specification of a numerical value and a direction. For example, specifying the value of the velocity is not enough to understand the movement of an object.

Vector

A vector is a quantity that has two independent properties: magnitude and direction. Vector also shows the mathematical or geometrical determination of such a quantity.

A vector is a physical quantity that has magnitude and direction as well. Magnitude defines the size of the vector. Vector is denoted by a line with an arrow, where the length of the line represents the magnitude of the vector and the arrow indicates the direction.

Vector Quantity

Vector Quantity is a physical quantity having magnitude with definite unit and fixed direction. Therefore, specifying the direction of action with its magnitude is important when we define any vector quantity. Displacement, weight, force, velocity, and more are some of the examples of vector quantities which have direction and magnitude as well.

Vectors Operations

Since vectors involve directions, these quantities must be taken in such a way that their directions are considered. The fundamental algebra rules do not apply to vectors in, such as when we simply add the values of magnitude ​​of the two vectors, then it gives the wrong result in most instances. 

The following operations are common operations which performed on vectors in the field of physics and maths:

1. Addition and Subtraction of two Vectors.
2. Multiplication of Vector quantity with Scalar quantity.
3. Product of the two vectors:

1. 1. Dot Product
   2. Cross-Product

Vector Resolution

Resolution of vectors means the splitting of vectors into many parts. These parts are called the components of the vectors.

A vector has two components, namely horizontal component and vertical component. is cos defined the value of horizontal component while sin represents the value of the vertical component.

Component of the vector along x – axis is termed as x – component.

Component of the vector along y – axis is termed as y – component.

Component of the vector along z – axis is termed as z – component.

There are two laws which are used for the addition of vectors. These laws are given as

1. Parallelogram Law of Vector Addition
2. Triangular Law of Vector Addition

Parallelogram Law of Vector Resolution

The parallelogram law of vector resolution includes using an accurately drawn, scaled vector diagram to define the components of a vector. The process includes drawing the vector to scale in the given direction, sketching a parallelogram around the vector so that the vector is the diagonal of parallelogram, and determining the magnitude of components (the sides of parallelogram) by using the scale.

According to parallelogram law of vector resolution, when opposite sides of a parallelogram formed from a locus can denote two vectors acting simultaneously in magnitude and direction at that point, then the diagonal of parallelogram which crosses that point can be used to define the resultant vector in magnitude and direction.

Triangle Law of Vector Addition

According to the triangle law of vector addition, when two vectors are denoted by the two sides of a triangle having the same order of magnitude and direction, then the third side of the triangle will denote the magnitude and direction of the resulting vector.

When two vectors are arranged such that the head of one vector is attached with the tail of the second vector then the triangle law of vector addition is used.

Types of Vectors

They are the following types of vectors which are given here.

Collinear Vector

Collinear vector is the type of vector where there are two or more than two vectors that are parallel to each other regardless of magnitude or direction. The collinear vectors never cross each other. The nature of direction of both vectors is the same.

The coordinates of both vectors are similar. The other property of the collinear vector is that the cross product of both collinear vectors is always zero. The collinear vectors are also considered as parallel vectors.

Zero Vector

The zero vector is a type of vector where the magnitude of the vector is zero and the origin point of the vector coincides with the end point. The direction of a zero vector is indeterminate and magnitude is always zero. The zero vector does not point in any direction and also has all zero components.

Position Vectors

Position vector is a type of vector where the origin point is 0 and there is an arbitrary point called A in space. Then the OA¬vector is termed as a position vector with reference origin 0. The position vector is basically used to indicate the location or position of the point in the 3D Cartesian dimension system. And the position is determined by each reference origin.

Conclusion

Physical quantities can be divided into two categories, namely scalars and vectors.

A vector is a quantity that has two independent properties: magnitude and direction.

Vector Quantity is a physical quantity having magnitude with definite unit and fixed direction.

The following operations are common operations which performed on vectors in the field of physics and maths:

1. Addition and Subtraction of two Vectors.
2. Multiplication of Vector quantity with Scalar quantity.
3. Product of the two vectors:

1. 1. Dot Product
   2. Cross-Product

Resolution of vectors means the splitting of vectors into many parts.

A vector has two components, namely horizontal component and vertical component.