444 



PRACTICAL MATHEMATICS 



Thus the effect of multiplying two vectors is to give rise to two 

 distinct products : 



(1) The product p^p 2 cos a ; this is the " scalar product/' and 

 must be taken in a direction corresponding to either of the lines 

 of action of the vectors. 



(2) The product p t p 2 sin a ; this is the " vector product," and 

 must be taken in a direction perpendicular to the plane containing 

 the lines of action of the vectors. 



EXAMPLES XXIV 



(1) A and B are two vectors ; if A = 83^ and B = 5 77 , find 

 (1) A + B and (2) A - B. 



(2) A and B are two vectors ; if A = 13 57 and B = 22 231 , find 

 (1) A + B and (2) A - B. 



(3) Find the components of a vector of magnitude 12 along direc- 

 tions which make angles of 25 and 55 with the line of action of 

 the vector. 



(4) A and B are two vectors ; if A = 12 35 , find B so that 

 A + B = 17 50 . 



(5) A and B are two vectors : if A = 14 40 , find B so that 

 A-B = 6 l5 o. 



A, B, C, and D are four vectors whose magnitudes and directions 

 are given in the table below : 



(6) Find A + B + C + D. 



(7) Find A - B + C - D. 



(8) Find A - B - C + D. 



(9) Working with the three vectors A, B, and C given in the 

 example of paragraph 210. Find B + C A. 



A, B, and C are three vectors whose magnitudes and positions 

 in space are given in the table below : 



