Introduction To Scalars & Vectors

SCALAR QUANTITIES

“Physical quantities which can completely be specified by a number (magnitude) having an appropriate unit are known as "SCALAR QUANTITIES".

Scalar quantities do not need direction for their description.
Scalar quantities are comparable only when they have the same physical dimensions.
Two or more than two scalar quantities measured in the same system of units are equal if they have the same magnitude and sign.
Scalar quantities are denoted by letters in ordinary type.
Scalar quantities are added, subtracted, multiplied or divided by the simple rules of algebra

EXAMPLES

Work, energy, electric flux, volume, refractive index, time, speed, electric potential, potential difference, viscosity, density, power, mass, distance, temperature, electric charge, electric flux etc.


VECTORS QUANTITIES

“Physical quantities having both magnitude and direction with appropriate unit are known as "VECTOR QUANTITIES”

We can't specify a vector quantity without mention of direction. 
Vector quantities are expressed by using bold letters with arrow sign such as:

Vector quantities cannot be added, subtracted, multiplied or divided by the simple rules of algebra.

Vector quantities added, subtracted, multiplied or divided by the rules of trigonometry and geometry.

                                  

PARALLELOGRAM LAW OF VECTOR ADDITION

According to the parallelogram law of vector addition:

"If two vector quantities are represented by two adjacent sides or a parallelogram then the diagonal of parallelogram will be equal to the resultant of these two vectors."

RESOLUTION OF VECTOR

DEFINITION

The process of splitting a vector into various parts or components is called "RESOLUTION OF VECTOR" These parts of a vector may act in different directions and are called "components of vector".

We can resolve a vector into a number of components. Generally there are three components of vectors.

Component along X-axis called x-component

Component along Y-axis called Y-component

Component along Z-axis called Z-component

Here we will discuss only two components x-component & Y-component which are perpendicular to each other. These components are called rectangular components of vector.

MULTIPLICATION OF A VECTOR BY A SCALAR

When a vector is multiplied by a positive number (for example 2, 3, 5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector.

If however a vector is multiplied by a negative number (for example -2, -3,  -5, -60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed.

DIVISION OF A VECTOR  BY A SCALAR

The division of a vector by a scalar number (n) involves the multiplication of the vector by the reciprocal of the number (n) which generates a new vector.

Let n represents a number or scalar and m is its reciprocal then the new vector is given by:

ADDITION OF VECTORS BY HEAD TO TAIL METHOD 

(GRAPHICAL METHOD)

Head to Tail method or graphical method is one of the easiest method used to find the resultant vector of two or more than two vectors.