CHAPTER XXIV 



205. The Vector. A vector is a quantity involving magnitude 

 and direction, and in dealing with it as much importance must 

 be placed upon its direction as is placed upon its magnitude. A 

 force, a displacement, a velocity, an acceleration are examples of 

 vectors, inasmuch as they have both magnitude and direction ; 

 while in the case of a velocity and an acceleration the magnitude 

 and the direction can each be functions of the time. If, for ex- 

 ample, a body is describing a circular path with uniform angular 

 velocity, the linear velocity of the body at any instant is a vector 



FIG. 138. 



of constant magnitude and of varying direction ; this direction 

 is directly proportional to the time. 



The four things which completely specify a vector are : 



(1) The point of application. 



(2) The magnitude. 



(3) The line of action. 



(4) The sense, or the direction along the line of action. 

 The " line of action " is determined by the angle it makes with 



some fixed direction, and usually this fixed direction is taken to 

 be horizontal. The " sense " is fixed according as the vector 

 acts away from or towards the point of application. Consequently 

 a vector can be represented graphically by means of a straight line ; 

 for let p be the magnitude, the direction, and the sense be posi- 

 tive, that is, the vector acts away from the point of application. 

 Let O be the point of application, OX the horizontal direction, 



/\ 



and OA the line of action of the vector. If XOA =6, OP =p to 

 some convenient scale, and the arrow indicates that the vector 



426 



