430 



PRACTICAL MATHEMATICS 



polygon be drawn, the closing line Oc x will give the sum of the 

 vectors A, B, C, and D, just as well as drawing the parallelogram 

 of vectors time after time. It should be noticed that although 

 the sense of each vector forming the sides of the polygon follow 

 a cyclic order, the sense of the vector sum, or the closing side of 

 the polygon, must be in the opposite cyclic direction. 



If one of the vectors is to be subtracted its sense must be reversed, 

 and the work can be proceeded with as in the case of addition. 



FIG. 142. 



Example. A, B, C, and D are four vectors whose magnitudes 

 and direction are given in the table below 



A 

 B 

 C 

 D 



30 



90 



150 



300 



Find (1) A + B + C +- D, (2) A + B - C + D, (3) A - B -f C - D. 



Fig. 143 shows the vector polygons drawn to scale ; the scale 

 of magnitudes being shown at the bottom of the diagram. By 

 actual measurement 



(1) A + B + C f D 



Magnitude = 9-1 

 Direction = 83 



(2) A + B - C + D 



Magnitude = 11-9 

 Direction =15 



(3) A - B + C - D 



Magnitude = 3-5 

 Direction = 146 C 



