**TWO DIMENSIONAL FORCE SYSTEMS**

Force F is resolved into two rectangular forces F _{x} and F _{y} as shown in Fig. 3.1.

F =F _{x} +F _{y}

F_{ x} and F _{y} may further be written as a scalar times the appropriate unit vectors i, j in two dimensions (x and y directions respectively).

where F _{x} and F _{y} are scalar components of the vector F in x and y directions respectively.

F _{x}= F cos θ

F _{y} = F sin θ

F_{2} (cos^{2} θ + sin^{2} θ) = F^{1 }+ F^{2}

F = √Fx^{2}+Fy^{2}

And θ tan ^{-1} F _{y} / F _{x}

The unit vectors in – x and – y directions are – and – j. So, – F _{x }i = F x (- i) ; it means that F_{x} in the- x direction. So in i, J and k system, the directions of F _{x}, F _{y} and F _{z} can be found easily.

Refer Fig. 3.2.

The resultant of the two forces F _{1}and F_{2} is

_{2y}; acts in negative y direction which is having unit vector-

where R _{x} and R _{y} are related to and the x and y components of R.