When we take a measurement of a parameter, the result is always a number. Only when the correct unit is supplied does this number make sense. As a result, a measurement’s result has a numerical value as well as a unit of measurement.

A body’s mass, for example, is 3 kilograms. A quantity with the numerical value 3 and the unit of measurement kg are used in this example. The magnitude is the numerical value combined with the unit. For the comprehensive description of some physical quantities, only magnitude is required. Magnitudes include body mass, distance between two places, time, temperature, height, the number of pendulum swings, and the number of books in a bag. They don’t have any sense of direction. Scalar quantities are those that have a single magnitude for their whole specification.

Other physical quantities, such as displacement, require a direction with magnitude to be described. Consider a body that moves from point X to point Y. The displacement is denoted by the letters XY. When the body moves from Y to X, however, the displacement is YX.

Vectors are quantities that need both magnitude and direction in order to be fully specified. Momentum, force, torque, magnetic field, and other vector quantities are examples.

Classification of vectors

1. Zero or Null Vector: A zero or null vector is one whose initial and terminal points are the same. This vector has no clear direction and has a magnitude of zero. It is represented by the number 0. Null vectors include the velocity of a stationary object, the acceleration of an item moving with uniform velocity, and the resultant of two equal and opposing vectors.
2. Unit vector: A unit vector is defined as a vector with a magnitude of one. A=AA is a unit vector in the direction of vector A. A unit vector is a direction-only vector that is both unitless and dimensionless.
3. Free Vectors: A vector is said to be free if its initial point is not specified. A non-localized vector is another name for it.
4. Negative of a Vector: The negative of a vector is a vector of the same magnitude as a given vector ‘a’ but in the opposite direction. It is denoted by –a.

b=–a

1. Like and Unlike Vectors: When vectors have the same direction, they are said to be like, and when they have the opposite direction, they are said to be unlike.
2. Collinear or Parallel Vectors: Collinear vectors are vectors that have the same or parallel supports.
3. Co-initial Vectors: Co-initial vectors are those that have the same initial point.
4. Coplanar Vectors: If the supports of a system of vectors are parallel to the same plane, the system is said to be coplanar. Non-coplanar vectors are the opposite of coplanar vectors.
5. Equal vectors: If two equal vectors a and b have the same size and direction independent of their initial location, they are expressed as a=b.
6. Negative vectors: Negative vectors are two vectors of identical magnitude but pointing in opposing directions.

Magnitude of vector

Vertical lines on both sides of the provided vector “|a|” illustrate the magnitude of a vector. It represents the vector’s length. The magnitude of a vector is calculated mathematically using the “Pythagoras Theorem,” i.e., b=x2+y2

Vector addition

One of the vector addition laws is the triangle law of vector addition. Because vectors do not obey ordinary algebraic principles, vector addition is specified as the geometrical combination of two or more vectors. The composition of a vector is the resultant vector.

The laws of vector addition are as follows:

1. Triangle law of vector addition
2. Parallelogram law of vector addition.

Triangle law of vector addition

The triangle law of vector addition says that when two vectors are expressed as two sides of a triangle with the same order of magnitude and direction, the direction and magnitude of the resultant vector is represented by the third side of the triangle.

Applications of vectors

1. Vectors are commonly used to navigate by air and by boat.
2. Planes are given a travel vector and must calculate how far they must go before turning or landing based on their speed. A sequence of vectors is used to create flight plans.
3. Vectors are used in sports instructions.

Conclusion

A vector is a mathematical representation of physical quantities that may be calculated in both magnitude and direction. A straight line with an arrowhead represents a vector of any physical quantity. The magnitude of the vector is determined by the length of the straight line, and the direction is determined by the arrowhead. If the magnitude and direction of two vectors are equal, they are considered identical vectors. The force applied to an object is the finest example of a vector since both the strength and direction of the applied force affect the object’s action. A vector’s magnitude will never change if it is rotated or moved around itself.