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42-43        ARMY AIR FORCES

c. Representation of a vector.—Although a vector is determined by two quantities, it can be represented graphically by an arrow having a length which depends on the magnitude of the vector and a direction which is the given direction.

(1) To find the proper length for a vector, a scale must be chosen arbitrarily, and some appropriate length must be selected to represent the given magnitude. A scale should be chosen which will give the best sized diagram. Large diagrams give more accurate results. For example, if 1 inch represents 100 pounds of force, a line 2 1/4 inches long would stand for a force of 225 pounds.

(2) The direction is measured clockwise from the north.

43. Addition of vectors.—a. The sum of two vectors, V1 and V2, is a third vector which is written V3 = V1 + V2. This is called the resultant of V1 and V2.

b. The resultant, when applied alone, gives the same result obtained by applying the two original vectors separately.

(1) To add two vectors, V1 and V2, graphically, draw both from a point O, then complete the parallelogram which has V1 and V2 as two of its sides. An arrow from O to the opposite vertex of the parallelogram which has V1 and V2 as two of its sides. An arrow from O to the opposite vertex of the parallelogram is the resultant. 

(2) Example: To add the vectors V1 and V2:

[[image - graphical method of adding vectors]]
Figure 50.

(V3 is the sum or resultant of V1 and V2.)

c. An alternate method of adding vectors is drawing V1 = OA from any point, O, and V2 = AB from the arrow end of V1, with arrow away from arrow end of V1. Then join O and B by an arrow. V3 = OB is the resultant. This method may be used to add any number of vectors. Merely add each vector to the preceding vector. The

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