VECTOK ADDITION. 



47 



and its magnitude is \/a* -f 6 2 ; also its inclination to Ox is 

 given by 



tan 9 = b 



In the same way - a + kb represents a vector lying in the 

 quadrant yOx' ; - a - kb, one lying in the quadrant x'Oij ; and 

 a kb, one lying in the quadrant y'Ox. 



36. Vector Addition. - If PQ (Fig. 13) is another vector 

 whose components parallel to Ox and Oy are respectively PA' 

 = NM = a and KQ = b'k, then the vector PQ is represented by 

 a -f- kb', and the vector OQ, which is the sum of the vectors OP 

 and PQ, is given by 



OQ = OM + MQ 



= (ON + NM) + (MK + KQ) 



= ( a + a') -f (kb + kb') 

 = (a + a 1 ) + k(b + V) 



This gives the law of vector addition, and inherently contains 

 that of subtraction also, the difference of the vectors OP and PQ 

 being represented by 



(a - a') -f k(b - ?/) 



