What is the use of dot product vectors?

Dot product is a convenient way to find the 'total impact' created by 2 different vectors whenever 2 vectors together have an impact in each others direction only,and no there is impact of one vector in perpendicular to the direction of other.

Let us understand this through the 'work done' by a force.

A force can change motion only in direction in which that force is applied.U cannot move a bode due east by applying a force due north.

So if we were to check the total impact of force applying body on the body upon which force is applied we can define a quantity as 'work done by force applying body'.obviously the impact is more either if the force is more or if the force is applied for a longer time( then body on which force is applied will accelerate longer)

.so 'work done by body applying force ' is 'force applied on body X distance moved by that body'

since cosine of a vector give the component of vector in direction of other vector.so we define work done as their dot product.by this way we automatically neglect the component of vectors perpendicular to each and only take the vector components in each others direction.

and since impact of any 2 quantities do not have any direction so we say that "dot product of 2 vectors is a SCALAR"

Actually the whole history of vectors revolve around physics and so we can understand logic behind vectors (actually a very big part of mathematics ) through physics.

I think that is a good example of use of mathematics for simplifying our everyday observations !!!!!!

It gives you a convenient way to calculate the component of one vector in the direction of another vector.

When use just need to now force and not the direction where the force is applied