Physics SCALARS AND VECTORS
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SCALARS AND VECTORS

Vectors-Introduction

Physical Quantities :

A physical quantity is a physical property of a phenomenon , body or substance that can be quantified by measurement by the measuring instrument. e.g., Length, Temperature, Velocity, Momentum etc.

They are classified into two parts usually.

1. Scalar quantity
2. Vector quantity

`text(Scalar Quantity :)`
A physical quantity which can be described completely by its magnitude only and does not require a direction is known as a scalar quantity. It obeys the ordinary rules of algebra. e.g.: distance, mass, time, speed, density, volume, temperature. current etc.

`text(Vector Quantity:)`
A physical quantity which requires magnitude and a particular direction and obeying laws of vector algebra, known as vector quantity. eg: displacement. velocity, acceleration, force etc.

A vector is represented by putting an arrow (bar) over it. The length of the line drawn in a convenient scale represents the magnitude of the vector. The direction of the vector quantity is depicted by placing an arrow at the end of the line. Its length is proportional to its magnitude, with respect to a suitably chosen scale.

`vec A` is a vector and `vec A=vec (PQ)=vec A=vec (PQ)`

Magnitude of `vec A=|vec A|` or `A`

Types of Vectors :

1. Parallel Vectors :
If two vectors have the same direction, they are parallel. No matter where they are locatedin space . Angle between the vectors will be zero. i.e. `vec a || vec b`

2. Equal Vectors :
Two vectors `vec a` and `vec b` are said to be equal when they have equal magnitudes and same direction. No matter where they are located in space. i.e., `vec a=vec b`

3. Anti - Parallel Vectors :
When two vectors `vec a` and `vec b` have opposite directions, whether their magnitudes are the same or not , we say that they are anti-parallel vectors .

4. Opposite Vectors :
The opposite of a vector is defined as a vector having the same magnitude as the original vector but the opposite direction. It is also said Negative of a vector.

5. Collinear Vectors :
When the vectors under consideration are along the same line are said to be collinear vectors. Angle between the vectors may be zero or `180^(circ)`.

`vec a, vec b` and `vec c` are collinear vectors.

6. Normal Vectors :
If two vectors are perpendicular to each other.they are normal vectors. No matter where they are located in space. Angle between the vectors will be zero. i.e `vec a bot vec b`

7. Unit Vector :
A vector having magnitude equal to unity with no units. It is represented by `vec a` . To find the unit vector in the direction of a. we divide the given vector by its magnitude. i.e. , `vec a = vec a/(|vec a|)` or `vec a = |a| vec a` or `vec a = a vec a`. where `|vec a|` or `a` is the magnitude of the vector `vec a` . Unit vector is basically used to indicate the direction

8. Zero Vector `(vec 0)` :
A vector having zero magnitude and arbitrary direction (not known to us) is a zero vector. It is also known as Null vector. It cannot represent graphically. It is used for the definition of Subtraction of vectors and Cross Multiplication of Collinear vectors ..

9. Axial Vectors:
These represent rotational effects and are always along the axis of rotation in accordance with right hand screw rule. Angular velocity, torque and angular momentum, etc .. are example of physical quantities of this type.

10. Coplanar Vector :
Three (or more) vectors are called coplanar vector if they lie in the same plane. Two (free) vectors are always coplanar.

 
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