RECTANGULAR COMPONENT OF A VECTOR

DEFINITION
DEFENITION 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 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

The parts of a vector resolved into vertical and horizontal vector are rectangular components. Rectangular components are perpendicular to each other.

Draw the X-Y axis for rectangular components as in figure (1).

From figure (1), it represents a resultant vector  on point . Through point O, it separates two components in X and Y direction axis. The two components are  and  on vector point ON and OM respectively. From point P draw two lines in X and Y axis as PM and PN.

The triangle law of vectors can be applied on a triangle ONP.

Where, the components of A are Ax in X-direction and Ay in Y-direction.

From triangle ONP find the value of cos q and sin q.

Add equations (1) and (2) and square it both sides.

Write the magnitude of given vector A.