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°