 In today's lecture, we are going to study composition of two force system which is nothing but the law of parallelogram of forces. At the end of this video, the viewers will able to derive the expression for the resultant force by using law of parallelogram of forces and to determine the resultant of the two force system. Here, if you observe this figure, all these forces are passing through a same point and in a same plane. So, when all the forces lie in a single plane and pass through a single point is known as co-planar concurrent force system composition of forces when the number of forces acting on the body there is a single force present which will give the same effect that of number of forces acting on the body such a single force is known as resultant force. Here if you observe these forces these are passing through the same point means these are concurrent forces in different direction means the direction of these all forces is where is now these all forces are acting on a body. Instead of these all forces one more force will present which will act on the body and which will give the same effect with by that of given by this all number of forces. So, to find that same effect the force which is called as resultant force and the force process of finding the resultant force is called as composition of forces. Composition of two force system if you observe this figure in this figure there are two forces F1 and F2 are acting on a body making an angle theta with each other. Now, where F1 and F2 are acting at theta with each other. So, if you draw the parallelogram by using force F1 and F2 here force F1 is nothing but horizontal force and force F2 is the force which will make the angle theta with F1. So, in this figure if you draw the parallelogram by using F1 and F2 you will get the parallelogram A, B, C and D and the diagonal of this parallelogram is nothing but the resultant force of the force F1 and F2 means whatever effect is given by the force F1 and F2 on this body the same effect will give given by the resultant force given by the resultant force. So, how you will find this resultant force here I will draw the perpendicular line from the point C. So, when we extend this line A, B line A, B is nothing but force F1 and line A, D is nothing but force F2. So, whenever you will draw the perpendicular line from point C you have to extend the line A, B up to point E. So, here you will get the right angle triangle A, E and C. So, to find the resultant force which will nothing but the hypothesis of the triangle A, E and C. So, if it is rectangle triangle. So, how we will find the resultant? So, we will find the resultant by using Pythagoras theorem. What is the Pythagoras theorem? It is under root adjacent square plus. So, here we will find this resultant force by using Pythagoras theorem. So, what is the Pythagoras theorem? It is under root adjacent square plus opposite square. So, here resultant force is equal to A, E square plus C, E square. Here if you observe this line A, E it is nothing but AB plus BE. So, you will get AB plus BE bracket square plus CE square. But as I told AB is nothing but force F1 and AD is nothing but force F2. Here if you find the value of BE it is BE is equal to BC cos theta. So, what is BE here? It is BC cos theta. So, BC is nothing but the force F2. So, here BE is equal to F2 cos theta and similarly the CE is equal to BC sin theta which is equal to F2 sin theta. So, by putting these values in the above equation you will get resultant R is equal to under root F1 plus F2 cos theta bracket square plus F2 sin theta bracket square. So, further which will give resultant is equal to under root F1 square plus 2 F1 F2 cos theta plus F2 square cos square theta plus F2 square sin square theta. If you observe this F2 square cos square theta plus F2 square sin square theta from this you will get F2 is common and cos square theta plus sin square theta is equal to 1. So, this equation is reduces to R is equal to under root F1 square plus 2 F1 F2 cos theta plus F2 square. So, finally you will get the resultant is under root F1 square plus 2 F1 F2 cos theta plus F2 square. So, it is the final equation to find the resultant force. Now, you have to find the inclination of this resultant force means R is making angle alpha with the line AB or with respect to force F1. So, to find the inclination of force resultant force you have to consider tan alpha is equal to y by x normally we will find alpha is equal to tan inverse of y by x. So, here we will consider the same concept and we will find out the inclination of resultant force. So, you will get tan alpha is equal to CE upon AE then tan alpha is equal to CE upon AB plus BA because A is combination of AB plus AE. So, here you will get AB plus BA. So, tan alpha is equal to CE is nothing but F2 sin theta divided by F1 plus F2 cos theta. So, finally this equation reduces to alpha is equal to tan inverse of F2 sin theta divided by F1 plus F2 cos theta. Now, so these are the some standard cases to find the resultant force of two forces. If you observe here figure A is showing that force F1 and F2 are making angle with each other 90 degree. So, when the theta is 90 degree between F1 and F2 you will get resultant force R is equal to under root F1 square plus F2 square. If you observe figure B and C here the theta is 180 degree. If you observe figure B and figure C here the angle which is made by F1 and F2 is 180 degree, but in figure B the direction of both the forces are same and in figure C the direction of both the forces is different. So, in that case for figure B the resultant force R is equal to under root F1 square plus 2 F1 F2 plus F2 square and when these two forces acting opposite to each other then resultant force is equal to F1 square minus 2 F1 F2 plus F2 square. So, these are the some standard cases considered for the these various types of force system. Now, by using the above equation you have used try to solve this problem. Here the resultant of two forces one of which is three times the other is 300 Newton when the direction of smaller force is reversed the resultant is 200 Newton. Determine the two forces and the angle between them. So, in this problem what they have mentioned there are two forces which are same means F1 is equal to three times F2 means they have indicated that one of which is three times of other is 300 Newton. It is the first case and the second case is when the direction of smaller force is reversed the resultant force is 200 Newton. So, here they have mentioned the resultant. So, you have to find out the force F1 and F2 and the inclination of the force. Here in this problem they have given the resultant force in above lecture we have studied how to find the resultant force from the two given forces, but here they have given the resultant force, but there are two cases when the resultant force is 300 Newton and the resultant force is 200 Newton. So, you have to find out the force F1 and F2. So, these are the answers that is F1 is equal to 80.6 Newton, F2 is equal to 241.8 Newton and the inclination of the resultant is 50.13 degree. So, these are the references considered for the study. Thank you.