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# Vector

Top
 Sub Topics You needs a lot of things to express anything in physics. Physics world is all about expressing the facts behind the qualitative and quantitative models. Quantitative facts can be expressed using physical quantities like speed displacement, temperature, length etc.There are basically two types of physical quantities - scalars and vectors. vectors tells about magnitude and direction of any physical quantity. The resultant is that what we get by combining the vector components. They are many vector quantities like displacement, velocity, acceleration, momentum, force etc. Lets study more about this.

## Unit Vector

It is a type of vector having magnitude as one. It is expressed with hat given as $\hat{a}$ where $\hat{a}$ = 1. It always indicates a specific direction.
It is given as
Here a is the given vector, |a| is the magnitude of vector a and $\hat{a}$ is the unit vector.

## Zero Vector

Zero vector called as null vector is that vector having magnitude as zero in any arbitrary direction. It is represented as $\vec{0}$. Its a dot with zero displacement. Fig below represents it

## Parallel Vector

Parallel vector word itself tells that the vectors are parallel. Two vectors are parallel if they have same or opposite direction. Their cross product is always zero. Figure below illustrates it :

If $\vec{a}$ and $\vec{b}$ are the parallel vectors then

The vector addition is a mathematical way of adding two vectors to get the resultant. They can only be added if they are directed in same direction. Vector addition can be using triangle law of vector addition and parallelogram of vector addition.

If $\vec{a}$ and $\vec{b}$ are the vectors given then the vector addition will be the magnitude of two given vectors. The vector addition is

## Vector Subtraction

Vector subtraction is operating the subtraction operation for the given vectors. This operation is for the vectors directed in opposite direction.

If $\vec{a}$ and $\vec{b}$ are given vectors then Vector subtraction is

## Vector Multiplication

Vector multiplication is multiplying the vectors that changes in magnitude but it does not alter its direction.

There are two types of vector multiplication
1. Cross product
2. Dot product.

## Vector Dot Product

The dot product for two vectors $\vec{a}$ and $\vec{b}$ is
Here $\theta$ is the angle between the given two vectors $\vec{a}$ and $\vec{b}$.
If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$ then cross product is