RESOLUTION OF VECTOR

RESOLUTION OF VECTOR

DEFINITION

The process of splitting a vector into various parts or components is called “RESOLUTION OF VECTOR”

These parts of a vector may act in different directions and are called “components of vector”.

We can resolve a vector into a number of components. Generally there are three components of vector viz.
Component along X-axis called x-component
Component along Y-axis called Y-component
Component along Z-axis called Z-component

Here we will discuss only two components x-component & Y-component which are perpendicular to each other.These components are called rectangular components of vector.

METHOD OF RESOLVING
A VECTOR INTO
RECTANGULAR COMPONENTS

Consider a vector

acting at a point making an angle q with positive X-axis. Vector is
represented by a line OA. From point A draw a perpendicular AB on X-axis. Suppose OB and BA
represents two vectors. Vector OA is parallel to X-axis and vector BA is parallel to Y-axis. Magnitude
of these vectors are V_x and V_y respectively. By the method of head to tail we notice that the sum of these vectors is equal to vector

. Thus, V_x and V_y are the rectangular components of vector

.
V_x = Horizontal component of

.
V_y = Vertical component of