# Scalar and Vector Quantity examples

In mathematics, we encounter two important quantities known as scalar and vector

## Scalar Quantity:

Scalar is one that possesses the only magnitude. it can be specified by a number along with a unit. The quantities like mass, time, density, temperature, length, volume, speed, and work are examples of scalar.

## Vector Quantity:

Vector is one that possesses both magnitude and direction. The quantities like displacement, velocity, acceleration, weight, force, momentum, electric, and magnetic field are examples of vectors.

Now here we discuss the vector and their fundamental operation. We begin with a geometric interpretation of vectors in plane and space.

### Geometric Interpretation Of Vector:

A geometric vector is represented by a directed line segment AB with A is in its initial point and B in its terminal point. It is often found convention to denote a vector by an arrow and is written either as \overrightarrow{AB} or as a boldface symbol like v or in underline Form \underline v.

#### Magnitude of a vector

It is also called a length or norm of a vector. The magnitude of a vector \overrightarrow{AB} or \underline v is its absolute value and is written as \left|\overrightarrow{AB}\right| or simply AB or \left|\underline v\right|.

#### Unit Vector:

A unit vector is defined as a vector whose magnitude is unity. The unit vector of vector \underline v is written as \left|\widehat{\underline v}\right| (read as \underline v hat) and is defined by \widehat{\underline v}\;=\frac{\underline v}{\left|\underline v\right|}.

### Zero Or null Vector :

If terminal point B of a vector \overrightarrow{AB} coincides with its initial point A. Then magnitude AB = 0 and \overrightarrow{AB} = \underline0 which is called zero or null vector.

### Negative Vector:

two vectors are said to be negative of each other

if they have same magnitude but opposite direction

if \overrightarrow{AB\;\;}=\underline v then \overrightarrow{BA\;\;}=\overrightarrow{-AB}\;=-\underline{\;v}

and \left|\overrightarrow{BA}\right|\;=\;\left|\overrightarrow{-AB}\right|

## Multiplication of vector by a scalar:

as we know that the word scalar mean to a real number. multiplication of a vector \underline v by a scalar k is a vector whose magnitude is k times of that of \underline v .it is denoted by k \underline v .

if k is positive then \underline v and k \underline v are in the same direction.

if k is negative then \underline v and k \underline v are in opposite direction.

Equal vector