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 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 Vx and Vy respectively. By the method of head to tail 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 .
Vy
 = Vertical component of .
MAGNITUDE OF
HORIZONTAL COMPONENT
Consider right-angled triangle DOAB
MAGNITUDE OF
VERTICAL COMPONENT
Consider right-angled triangle DOAB