Question
What are rectangular components of a vector? How will you resolve the rectangular components of a vector in a plane?
Solution
When the resolved components of a vector are mutually perpendicular to each other, they are called as rectangular components.
Let us resolve the rectangular components of a vector.
The resultant of the vector is represented by
in XY plane.
Now, from point P, draw a perpendicular PM on X-axis and PN on Y-axis.
Now, using the triangle law of vectors to
we have
Let us resolve the rectangular components of a vector.
The resultant of the vector is represented by
in XY plane. Now, from point P, draw a perpendicular PM on X-axis and PN on Y-axis.
Now, using the triangle law of vectors to
we have Here, vectors OM and ON are mutually perpendicular to each other. Therefore, the vectors OM and ON are called rectangular components of vector R.
Now, using appropriate notations, X and Y components are represented by 
, respectively.
The internationally accepted notations for unit vectors along X-axis and Y-axis are 
respectively. Thus, 
If the vector 
has magnitude R, and makes an angle 
with positive direction of X-axis. The from 
