8,9] 



RESOLUTION. 



11 



axes of x, y, and z, and these are the resolved parts of the vector 

 in the directions of these axes. 



In the former case taking OP to represent the vector, and 

 drawing PM at right angles to Ox, OM and MP represent the 



Fig. 9. 



resolved parts of the vector parallel to the axes. If R is the 

 magnitude of the vector represented by OP, and 0, &amp;lt;f&amp;gt; the angles* 

 between the lines OP and Ox, Oy, then R cos 6 and R cos are 

 the magnitudes of the resolved parts respectively, and these are 

 the projections of OP on the axes. 



More generally, taking OP to represent the vector, and drawing 

 a parallelepiped with and P as opposite corners and with its 

 faces parallel to the coordinate planes, the resolved parts of the 

 vector in the directions of the axes are numerically equal to the 

 projections of OP on the axes. If R is the magnitude of the 

 vector represented by OP, and if I, m, n are the cosines of the 



* In Fig. 9 cos&amp;lt; is sin0, but it is easy 

 to draw a figure, e.g. Fig. 10, which makes it 

 appear that cos &amp;lt; is - sin 6. With the usual 

 conventions in regard to the signs of trigono 

 metrical functions we shall always have 



cos = sin 



provided 6 is the angle traced out by a line 

 OP starting from Ox and turning round O in 

 the direction Ox to Oy. 



Fig. 10. 



