 Hello friends. So in this session, we are going to talk about force being a vector quantity. So in the previous sessions, we saw or we defined force, we also defined the unit of force that is one Newton. Now we are going to talk about the nature of force as a physical quantity. And we did learn about vectors and scalars in our previous chapter where we knew or we came to know that vectors are physical quantities or vector quantities are those physical quantities which have both magnitude as well as direction and and yes, they also observe or follow some vector laws. So we came across different types of vector quantities. For example, we had a displacement. If you recall, we had displacement and the displacement was displacement was a vector quantity. Then we also had velocity. So velocity was a vector quantity as well. Acceleration, these were vector quantities which we have discussed already. So what is the specialty of a vector quantity? So all of them will have magnitude. That means they have some value magnitude and they also have direction. So direction is equally important. So those quantities which have magnitude as well as direction are called vectors. And we used to name them or notify them like A, B and arrow sign. So where A is this point A and B is the end of the vector, A is the start or this is A is the tail, B is the head and the arrow represents the direction whereas the length of the arrow depicted magnitude. So length depicted magnitude and this arrow depicted direction. So that's what we learned. So similarly here also force is also a vector quantity. So we can write force is a vector quantity and we can explain this using an example. How do we know that force is a vector quantity? So let us say in the tug of war, so you have participated let's say in a tug of war event where there is a rope and there is a kerchief in the middle of it and there are teams which are pulling the rope in two direction. So let's say F1 is the force applied here, F2 is the force applied in this direction and the kerchief is in the middle. So you know this is what happens in a tug of war. Now if you see the kerchief stays there if both the teams are applying same amount of force. Let's say this team is applying X Newton of force let's say 100 Newton force just for an example 100 Newton. 100 Newton is too small a force but let it be. So let's say another one here also they are applying 100 Newton. So if you can see both are same in magnitude both the forces are 100 Newton each but the kerchief is not moving at all or this point let's say P is not moving at all despite the fact that in magnitude wise there are 200 Newton force being applied on this point P. So that means we can very clearly see that this 100 Newton is cancelling out this 100 Newton. So hence the direction does matter right. Alternatively let's say if the same point P was here and you would have let's say pulled with 100 Newton force now and pushed also with 100 Newton force. Let's say P is an object or a person or anything and one you know like a railway engine let's say. So let's say there are lots of wagons which are connected and there's an engine which is pulling it you know in this direction this is let's say engine and there's another engine which is pushing from behind as well. So pushing it behind right. So both of them are actually augmenting their forces or helping each other to reinforce their forces right. So when both the forces are in the same direction they get added up so let's say if this was 100 Newton here and 100 Newton here then the total is very simply total force being applied is 200 Newton which is also called resultant force isn't it. This is called resultant or total resultant force right. So hence the another thing which we can talk about here is principle of superposition right. So there is something called principle of superposition of forces. What does this principle mean? Principle of superposition of forces. What does this mean? It means that you know all the individual forces can be replaced by one force which has the same effect as the individual effects. So for example this 100 Newton here and this 100 Newton here. So two engines are one is pulling by 100 Newton another was pushing by 100 Newton. So instead of these two engines you can simply replace both of them by one engine which can pull or push by 200 Newton then we say that this 200 Newton is the resultant of resultant force. So that means you this principle of superposition means you can replace all the forces acting on a body by a single force by the laws of vectors right. So we have learned that in the previous session. So by the laws of vectors we can replace all the individual forces by one single force and that is what we say that this is principle of superposition of forces. I hope you understood this. So hence dear friends what were we talking about? So forces are vector quantities if acting in the same direction they get added up if acting in the opposite direction they get subtracted and there's a third case where they are not in the one in one line of action. So for example if this is 100 Newton and let's say what happens if another force is acting like this. So let's say there's an object just to give you a practical case let's say you there are two friends of there are two friends one friend is pushing one object like this let's say 100 Newton force same 100 Newton he's applying in the east direction another one is trying to push with 100 Newton in the north direction. So what is the total force acting on it that means if I wish to replace these two forces by single one what will be that force and in which direction that force should be applied. So intuitively you could see that this particular object will tend to move in this direction so hence but then the total force which has to be applied to affect this change will not be 100 plus 100 that is 200 but it will be simply 100 root 2. How is this coming? This is by application of vectors which we need to spend some other session on understood. So for the time being you understand that if it if the forces are in the same direction then they simply get added up by the principle of superposition so 100 plus 100 there Newton Newton is equal to 200 Newton okay but 100 plus 100 sorry this direction 100 reverse direction 100 this is 100 this is going to give you zero Newton okay and you can do all the calculations let's say this is 200 and now this is 50 then this is equal to 150 Newton but the direction will be which one is more this one okay similarly let's say if we have here 200 and here 50 this direction then the resultant is here 150 in the west direction. I hope you understood this you know the operation on vectors so hence 100 plus 100 in the same direction just gets added up 200 100 and this 100 plus reverse 100 is simply 100 minus 100 so hence two directions are opposite 180 degrees apart so you'll get zero Newton 200 plus this reverse direction 50 Newton is something but negative 50 Newton so you'll get 150 in the in this direction and for this case it has to be 150 Newton in the best direction correct so I hope you understood the operation on vectors for the time being if the vectors are not in the same line for example as I told you if they are perpendicular you can apply Pythagoras theorem till this point you can solve it let's say this is 90 so the resultant we will learn in vector this is called triangle law vector addition so if this is 100 Newton my dear friends this is 100 Newton in these these two directions so this one will be the hypotenuse 100 root to Newton and this will be the resultant of this 100 and this 100 you can ask a question what happens if this is not in the 90 degrees line then what happens then we have to use the principles of trigonometry and geometry to find out this particular length so if this is a force this is b force so this is a plus b force okay so a plus b is resultant of this a added to this b okay so this is a separate topic of discussion we'll discuss it in some other session so in this discussion what did we understand so we understood that force is a vector quantity which has not only magnitude but also direction okay and forces get added up in one direction and get subtracted if they are in reverse direction and multiple vectors can be replaced by single vector by the principle of superposition of forces right so this is what we learned and then we saw some operations on vectors so two forces so two forces in the same direction will get added up if they are in the reverse direction they will get subtracted and it will simply you know we will be applying concepts of arithmetic to just get the resultant magnitude of vector okay so let's meet in the next session to talk further about forces