10 GEOMETRY OF VECTORS. [CHAP. II. 



where the edges of the parallelepiped are the axes of reference 

 relative to which the positions of points are determined. 



Fig. 8. 



9. Components and Resultant. A set of vectors equiva- 

 lent to a single vector are called components, and the single vector 

 to which they are equivalent is called their resultant. 



The operation of deriving a resultant vector from given com- 

 ponent vectors is called composition, we compound the components 

 to obtain the resultant ; the operation of deriving components in 

 particular directions from a given vector is called resolution, we 

 resolve the vector in the given directions to obtain the components 

 in those directions. 



It is clear from the constructions in the preceding article that 

 we can resolve a vector in one way into components parallel to 

 any two given lines which are in a plane to which the vector is 

 parallel, and again we can resolve the vector in one way into 

 components parallel to any three given lines not in the same 

 plane. 



When the directions of the component vectors are at right 

 angles to each other the components are called resolved parts of 

 the resultant vector in the corresponding directions. 



Thus, if we take a system of rectangular coordinate axes, any 

 vector parallel to a coordinate plane, e.g. the plane of (x, y\ can be 

 resolved into components parallel to the axes of oc and y, these are 

 the resolved parts of the vector in the directions of the axes of x 

 and y. 



Again, taking a three dimensional system of rectangular axes, 

 any vector can be resolved into components parallel to the 



