Vector Addition By Rectangular Components ( FSC part 1)

Vector Addition By Rectangular Components:
let A and B be two vectors which are representative by two directed lines ON and OM respectively. The Vectors B is added to A by the head to tail rule of vector additions.
So, the resultant vectors R = A + B is given, in direction and magnitude, by the vector OP.
    In the below fig Ax, Bx, and Rx are the components of the vectors of A, B and R and their magnitude are given by the line OQ, MS, And OR respectively But,
       
        OR = OQ + QR
    or    OR = OQ + MS
or        Rx = Ax + Bx

Similarly the sum of the magnitude  y-components of two vectors of the resultant that is

    Ry = Ay + By
since Rx and Ry are rectangular components of the resultant vector R, hence

    R = Rx i^ + Ry j^
    R = (Ax + Bx) i^ + (Ay + By ) j^
The magnitude of the resultant vector A is given in below fig.

    and the direction of the resultant vector is determined that show in below fig.

The vectors addition by rectangular components consists of the following steps.

(i). find y-components of all given vectors.

(ii). Find x- components Rx of the resultant vectors by adding the y-components of all the vectors.

( iii ). Find the magnitude of resultant vector R using below equation.

(iv). Find the direction of resultant vector R by using below equation.

In the Below Video lecture you can watch helpful contents.