Using the definition of the scalar product, find the angle between the following vectors. (find the smallest angle.)
a) a = 5i - 9j and b = 5i - 5j
(b) a = -8i + 5j and b = 3i - 4j + 2k
(c) a= -2i + 2j and b = 3j + 4k

The answer 
a)  a) A = 5i - 9j and B = 5i - 5j
scalar product definition
A.B= //A// //B// cos (A, B), so 

let X = (A, B) the angle
cos X = A.B  /   //A// //B// 

A.B = 25+45=70
//A// //B// = 72.80
cos X = 70/72.8  X= arccos (70/72.8)=90°

c) A= -2i + 2j and B = 3j + 4k

A.B= //A// //B// cos (A, B), so 

let X = (A, B) the angle
cos X = A.B  /   //A// //B// 
A.B=2
//A// //B// =14.14
cos X =0.14, X= arccos(0.14)= 81.9°