Question

Explain how a vector can be resolved into its rectangular components in three dimension

Answer 1

Answer:

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 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 .