Question

explain rectangular component of a vector show that working for where is accounted by a resolution of a vector

Answer 1

When vector got split into various parts or components, it is called resolution of the vector. When they act in different directions they are called components of the vector.A vector can be resolved into a number of components. Three components of vector are-
Component along X-axis called x-component
Component along Y-axis called Y-component
Component along Z-axis called Z-component
These components are commonly called rectangular components of the vector.

Working on resolving the vector into rectangular components-Consider a vector which is it a point making an angle q with +ve X-axis. 
Represent vector by a line OA.
From point A, draw a perpendicular AB on X-axis.
Suppose OB and BA represent two vectors.
Vector OA is parallel to X-axis
vector BA is parallel to Y-axis.
The magnitude of these vectors is Vx and Vy.
Applying head to tail method we notice that the sum of these vectors is equal to vector.
Thus Vx and Vy are the rectangular components of vector . 
Vx = Horizontal component of OB.
Vy = Vertical component of AB.

cosФ = OB/OA
OB = OA cosФ
Vx = V cosФ

sinФ = AB/OA
AB = OA sinФ
Vy = V sinФ