436 PRACTICAL MATHEMATICS 



. 10-263 



a=C S 1P38- 

 = 44 30' 



7-826 



14-38 

 = 57 2' 



. 6-357 



f =C S 14138 

 = 63 50' 



(2) To find A - B + C 



X = 4-3300 - 1-6904 + 4-2426 



= 6-8822 

 Y = 1-7100 - 3-3920 + 2-7240 



= 1-0420 



Z = 1-8240 - 1-2800 + 3-2526 

 = 3-7966 



P= A/6-8822 2 + 1-0420 2 + S-7966 2 

 = 7-929 



6-882 



7929 

 = 29 47' 



1-042 



= 82 27' 



. 3-797 



^ C S 7^29 

 = 60 53' 



211. The Scalar Product of two Vectors. The scalar product of 

 two vectors, taken in a given direction, is the product of the effec- 

 tive parts of the vectors in that direction ; that is, the algebraic 

 product of the components of the vectors in that direction. 



Taking two vectors, one of magnitude Pl and direction 6 X ; the 

 other of magnitude /o 2 and direction 2 . 



/\ /\ 



Let OX (Fig. 144) be the line of reference, PiOX = Q lt P 2 OX =0 2 



and POX = 8. Also let OP 1 = Pl and OP 2 = Pt . 



Then ONj = Pl cos (0 a - 0) 



and ON 2 = p 2 cos (0 2 0) 



are the components of the vectors taken in the direction OP. 



