let us answer our sample problem so this problem is the same as our as the problem used in the parallelogram method so we have here two forces acting on a particle force a is three newton's directed north and force b is four newtons directed 30 degrees north of east find the resultant force using the polygon method so our given we have force vector a which is three newton's north and then force vector b which is four newtons 30 degrees north of east so our first step is to assign a scale that would represent our quantity so we have here um a centimeter ruler where in every one centimeter we every one centimeter will represent one newton so therefore if i have six centimeters then that would mean that the magnitude of the vector is six newtons if i have four centimeters then the magnitude of the vector would be four newtons so therefore our scale to use is one centimeter is the one newton second step is to locate our given vectors in our gravitation plane so we utilize cartesian plane to visualize the direction of the vector so here we have force vector so we want to visualize and to visualize the directions of our force vectors using this cartesian plane so we have here north east south and west so vector a is three newton's north so ola associated direction given angle so since it is directed north then it is a straight line going towards the north going towards the north so three newtons so we need to count three centimeters because every centimeter represents one newton therefore three centimeters will represent three newtons so we have here one two three so this will be our vector a so three newtons north next is to sketch the succeeding vector so we only have two vectors here so therefore vector b is our last vector so vector b is said to be 30 degrees north of east so 4 newtons 30 degrees north of e so if if the vector is i know is at an angle exist at an angle so we need to measure first the angle and then followed by measuring um sketching the vector together with its magnitude so let's proceed with our next step which is to measure the angle of our vector surface and vector b is 30 degrees north of east so to compare the parallelogram and the polygon method in parallelogram method we sketch the vectors we draw the vectors from the same initial point so we're in that initial point is represented by the point of origin so if this is a parallelogram method then that vector b will be drawn from this point and then yeah gentile however since this is polygon method so polygon method utilizes the head to tail method or the tip-to-tail method wherein the succeeding vectors will be drawn from the tip or from the head of the previous vector so galling tayo detos of vector a our first vector then genta yo yanamagiging yung tipnyan will be our reference to measure 30 degrees angle so we have here our protractor and we already marked the 30 angle 30 degree angle so let us now draw force vector v so force vector b is four newton so therefore ayanna so let's count four centimeters and that will represent four newtons b and of course we're going to um align it from the tip of our previous vector to this 30 degree angle so mark indito and so this will be our vector b which is four newtons north of easter 30 degrees north of east so our next step is to close this i know close this diagram so this to create the polygon so we will need to close this and that closure represents the resultant vector so the resultant vector is drawn from the initial point directed towards the last drone vectors and while you're sketching you can already measure it then you can already measure the magnitude of your resultant vectors in this case we have a measure of six centimeters therefore your resultant vector has a magnitude of six newtons to find or to determine the direction we need to measure the angle of this vector with respect to the east line so let us now use again our protractor and measure the angle of resultant vector with respect to our east line so let's zoom this in so um it aligns the vector the resultant vector aligns with 55 degrees degree angle so therefore our resultant vector is 6 newtons 55 degrees north of east so diagram so we have here force vector a and then force vector b and then resultant vector when we add the force vector a and force vector b so sideways vector addition is vector one plus vector two and if we have more than two vectors then vector one vector plus vector two plus vector three and so on will be equal to the resultant vector so here a plus b is equal to r which is the resultant so 3 newtons north plus 4 newtons 30 degrees north of east is will result to 6 newtons 55 degrees north of east so this will be our final answer so in our next um examples we will see how to perform vector addition with with multiple vectors more than two vectors