VECTORS IN SPACE 19 



7T Vt 



make an angle - H with Ox, so that the components of the velocity 



along Ox, Oy, say v ly v z , will be 



/IT Vt\ Vt 



v* = V sin ( - H ) = V cos 



\2 a I a 



The acceleration along Ox is -> which, on differentiating v l with 

 respect to t, is found to be 



F 2 F 



cos , 



a a 



while that along Oy is similarly found to be > or 



F 2 . F* 



sin 



a a 



F 2 



Compounding th^ese, we obviously obtain an acceleration along BO, 



the result already obtained on page 15. 



Composition and Resolution of Vectors in Space 



15. It may be that the vectors to be compounded are not all in 

 one plane. However, the method of determining the resultant is 

 essentially the same. Thus we can con- 

 struct a polygon in space ABCD -> N 

 such that the sides AB, BC, , MN rep- 

 resent the vectors R^ -, R n . As in the 

 preceding case, it is readily shown that 

 AN is the resultant. 



It is usually more convenient to resolve 

 each vector into three components par- /y FIQ 



allel to rectangular axes in space. Given 



a vector AB, we draw through A, and likewise through B, three 

 planes parallel to the coordinate planes. They inclose a rectangular 

 parallelepiped of which AB is a diagonal. The edges AC, AD, 

 AE represent three vectors by which AB can be replaced ; they 

 are the components parallel to the axes of the vector AB. 



Suppose there are n vectors, and that the direction angles of 

 the vector R s are denoted by a s , /3 S) y s . As above, each vector R s 



