Resolution of a Vector Into Rectangular Components
Splitting up a single vector into its rectangular components is called the Resolution of a vector.
Components of a vector making an angle of 90º with each other are called rectangular components.
Let us consider a vector F represented by OA, making an angle O with the horizontal direction.
Draw perpendicular AB and AC from point on X and Y axes respectively. VectorsOBand OC represented by Fx and Fy are known as the rectangular components of F. From head to tail rule of vector addition.
OA =OB+ BA
F = Fx + Fy
To find the magnitude of Fx and Fy, consider the right angled triangle OBA.
Fx / F = Cos θ => Fx = F cos θ
Fy / F = sin θ => Fy = F sin θ