Perpendicular Components Method ?? EXPLAIN this method in detail with examples plz ..

Perpendicular Components Method

This method is usually used in the Cartesian plane, but can be used for other vectors too.

1.  
   Split each vector into two perpendicular components, for example horizontal and vertical components. It is usual to split vectors into components along the x-, and y-axes in the Cartesian plane. The unit vector along the x-axis is conventionally written as i, that along the y-axis as j.
   • 

      A 7N force resolved into components
     In order to resolve a force into components, you will need to know the angle that it makes with the horizontal, vertical, x-axis, or the y-axis. Once this angle is known, you can construct a right-angled triangle with the force as hypotenuse and the other two sides along the x- and y- axes. The lengths of the two other sides are the magnitudes of the components along those directions, and may be calculated using trigonometry. The side adjacent to the angle is xcos(angle), and the side opposite is xsin(angle), where x is the magnitude of the original force.
   • If a component points to the left or downwards, it is given a negative sign (-).
2.  
   Add all the magnitudes of the horizontal components (or those along the x-axis) together, and separately add all the magnitudes of the vertical components (or those along the y-axis). If a component has a negative sign (-), its magnitude is subtracted, rather than added.
3.  
   Calculate the magnitude of the resultant using the Pythagorean Theoremc²=a²+b², where c is the magnitude of the resultant vector, a is the magnitude of the sum of the components along the x-axis, and b is the magnitude of the sum of the components along the y-axis.
4.  
   Calculate the angle that the resultant makes with the horizontal (or the x-axis) by using the formula ?=tan^-1(b/a), where ? is the angle that the resultant makes with the x-axis or the horizontal.
5.  
   Represent your resultant vector. For example, if the vectors represented forces, then write "A force of x N at y^o to the horizontal/x-axis/etc".