PRODUCT OF TWO VECTORS. 51 



vector resulting from a rotation of the vector 

 OP through a right angle in the positive direc- 

 tion of rotation without any alteration of its 

 length. 



By similar reasoning we can show that k . OP represents 

 the vector resulting from a rotation of the vector OP through a 

 right angle in the negative (clockwise) direction of rotation. 



39. Definition of Lag and Lead. A vector OP is 

 said to lead before, or lag behind, a vector OQ, according as the 

 least amount of rotation necessary to bring OP into the same 

 direction as OQ is in the negative or positive direction. 



It follows, therefore, that the vector k . OP leads before the 

 vector OP by a right angle, and that the vector k . OP lags 

 behind the vector OP by a right angle. 



PROBLEMS ON CHAPTER VII. 



1 . Draw diagrams showing the following vectors : 



k, 1+k, 2 + 3*, -2- 3k, -2 + 3k. 



2. What is the sum of all the vectors in Question 1 ? 

 Answer. 1 + 6k. 



3. What is the product of each of the following pairs of vectors ? 



2 + 3k* 2 + 3k} -2-3kl - 2 - 3k'l 



3 + 3k] 3 -2k] 3 -2k] -3 -2k] 



Answers. 15; 0; 0; 12. 



