so how are we going to perform vector addition when two or more vectors are given so remember that we already have an example for for adding vectors for adding two vectors but how about when adding two or more more than two vectors so so we can use different methods in adding two or more vectors so we have the parallelogram method we also have the polygon method and we have the component method so in this in this video we are going to perform adding more than two vectors using the polygon method so using this problem so our sample problem number two four vectors show the direction of forces acting on a body so determine the magnitude and the direction of the resultant if force number one force vector one is 10 newtons 45 degrees north of east force vector 2 is 5 newtons 10 degrees south of east and force number three is six newton's east force four is six newtons 20 degrees south of west so we want to know our resultant force so the resultant force is unknown so let us use the scale of 0.5 cm is to 1 centimeter so therefore every every 5 centimeter in our ruler represents 1 newton so second step so of course is to locate the vectors in our um cartesian plane so again we use cartesian plane to visualize the direction so if you don't want to use the cartesian plane and you just want to measure that to draw the diagram of this vectors then you can also do it but in our case let us use the cartesian plane so that we will be guided with the direction of our vectors so let us draw first force vector number one so force vector number one is 10 newtons 45 degrees north of east so since it is at an angle then we need to measure first the angle so that we will be guided when we are measuring the magnitude so first yeah so mark the angle we have here anonym 45 degrees so therefore we'll use this as a reference for sketching 10 newtons 10 newtons of force so yeah so this will be our vector number one so sabina then every half centimeter or every zero point five centimeter represents one newton so therefore ato one newton two three 4 5 6 7 8 9 and 10 newtons so that will be our force vector number one so f of 1 is 10 newtons 45 degrees and our direction is north with respect to our east line so to guide us with sketching um our our succeeding vector vectors since the first vector is already existed exists at an angle another another force vector with an angle so let us create another smaller cartesian plane so there okay so from the tip of the anode from the tip of our previous vector let us draw yan meron new north east south and west for uh for sketching our next vector so so vector number two is five newtons 10 degrees south of east so asan bayong south of east so young south of east newton cartesian planet and smaller cartesian plane is here so yeah so we need to measure 10 degrees with respect to the east line of this cartesian plane so let us now use our protractor yeah to measure 10 degrees sumera not a hydro so we already marked the 10 degree angle so with respect to our east line so you know north east south and west so ally not any protractor with our cartesian plane and then measure 10 degrees 10 degrees nothing with respect to this smaller cartesian plane okay so since we already marked the angle let us now sketch a 5 newton force so nito again every half centimeter represents one newton so therefore at a one newton two three four and five so i'm gonna be too long you so that is our force vector number two which is five newtons 10 degrees south of east line so next step is to just repeat the process so since we have more than two vectors then previous vector succeeding vectors so let us now draw or another smaller cartesian plane again baby cartesian plane gen so let us let us use this smaller cartesian plane to locate force vector number three so of course vector number three is six newtons is since mulan among angle then you another force vector number three will just be a horizontal line straight horizontal line so three newtons i am i six newtons rather six newtons so therefore we have here one two three four five and six so that's our force vector number three and then for force vector number four so lini patna natin dito yo nothing i know smaller and down a little smaller cartesian plane worst vector number four is directed 20 degrees south of west so 20 degrees south of west sodito meron tayo and kardashian and south of west is here so somewhere here this since this is south and this is the west line we need to measure 20 degrees with respect to our west line so we have here 10 20. you mark 20 degree angle nothing so let us now sketch force vector number four which is six newtons south of west so now that we have uh the four vectors we have located the given vectors it is now time to close the polygon so the closure again so the last vector the drawing nothing will represent the resultant vector jung vector that will close the diagram so we'll create the polygon okay so from the initial point let us sketch the resultant vector so so while you are sketching you can already measure you can already measure the magnitude of your resultant vector so we have 1 2 3 4 5 6 7 8 9 10 11 12 13. so therefore the magnitude of our resultant vector resultant force vector is 13 newtons so i am so that will be our sultan vector which is 30 newtons so direction yeah so we need to look for the angle of this resultant vector with respect to our east line force resultant force vector with respect to our east line so let us now measure the angle so the angle of the resultant vector is again approximately nasa 18 degrees 20 this is 19 and and 18. in in real situation in real situation of course you need to i know you need to apply the uncertainties so little we're just estimating it assuming it to be approximately approximately 18 degrees actual situation you need to apply young previous concepts na na to tuna natin which is to apply the uncertainties and measurements so you apply an obayom padding maximum error or minimum error maximum uncertainty or minimum uncertainty but in this case we assume it to be 18 degrees 18 degrees with respect to our east line so i am so now we now know that our force vector at of our resultant force vector is 13 newtons 18 degrees and the direction is north of east line so north of east yen so kappa in a tensor force vector one plus force vector two plus force vector three plus the force vector for it will result to 13 newtons 18 degrees north of this line so unito are this one so independence lineage so each of these vectors ayan jung value so for example we have the particle here we have a particle here and then we have these forces acting on it force the diagram so we have a force vector which is i know which is 45 degrees north of east so 10 newton sha and then we have 6 newton acting towards east and then we have here 5 newton so and so applied 10 degrees south of east and then we have here our fourth vector force vector not images 6 newton 20 degrees out of west so for example they are a push um pushing force so debug because force can be a push or it can be a pole so subbing and nothing they are all pushing this particle so my own annoying final movement so given that these forces are applied to this particle so when we add all of those forces so when we add force one force to force three and then force four the resultant force is 13 newtons 18 degrees north of east so we expect that this anas this particle will move 18 degrees north of east since our resultant force is towards this direction so ayan young adding resultant force and then since janjung resultant force nothing then it will force our it will push our particle to move towards the same direction as our resultant force okay so that will end this um this solution for our sample problem number two so in our next um video we are going to discuss how to perform vector addition using component method