12 



GEOMETRY OF VECTORS. 



[CHAP. ii. 



angles which OP makes with Ox, Oy, Oz respectively the resolved 

 parts in these directions are Rl, Urn, and En respectively. 



Fig. 11. 



This rule determines the senses as well as the magnitudes of 

 the resolved parts ; thus, when cos 0, in the first case, and I, in 

 the second case, are negative, the component parallel to the x axis 

 is in the negative direction of that axis, i.e. in the direction xO 

 produced. 



It is clear from this rule that when the magnitudes and signs 

 of the resolved parts of a vector in the directions of three mutually 

 rectangular lines are given the vector is uniquely determinate, 

 that is to say there is one and only one vector which has given 

 resolved parts parallel to three such lines. 



The construction in the former of these cases is a construction 



for the resolved parts of a 

 vector parallel and perpen- 

 dicular to a line. As before, 

 let OP be a line representing 

 the vector, and OA a line 

 parallel and perpendicular 

 to which the vector is to be 



A resolved. Draw PM at right 



Fig. 9 a. angles to OA. Then the 



