CHAPTER VII. 



Algebraic Representation of VectorsVector Addition Products of Vectors. 



THE ELEMENTS OF VECTOR ALGEBRA. 



32. Any physical quantity which requires for its complete 

 specification data regarding (1) its magnitude, (2) its direc- 

 tion, and (3) its sense along that direction is called a vector 

 quantity. Quantities which are completely specified when their 

 magnitudes only are given are called scalar quantities. 



Mass and energy are examples of scalar quantities ; velocity, 

 acceleration, force, electric current, and electromotive force are 

 examples of vector quantities. 



Vector. A vector quantity may be completely represented 

 by a straight line drawn in a particular direction, the sense along 

 the direction being shown by means of an arrowhead, and the line 

 containing as many units of length as the quantity to be represented 

 contains units of quantity. 



We call a line drawn in this way a vector, e.g. the vector OP 

 (Fig. 11) may represent an electric current if its direction is repre- 

 sented by the direction of the line OP, its sense from to P along 

 this direction, and if OP contains as many units of length as the 

 number of amperes (or other unit of current) in the electric current. 



33. Equality Of Vectors. Two vectors are equal if they 

 contain the same number of 

 units of length, are parallel to 

 the same direction, and have 

 the same sense ; thus in Fig. 

 11 the vector OP is equal to 

 the vector O'P, if the length 

 of OP equals that of O'P, the 



, . IT 1 J FlG - 



two vectors being parallel and 



of the same sense. If the sense of a vector along a given 



direction is reversed, its sign is reversed, so that 



PO = - OP 

 or PO + OP = 



