Find the smallest positive angle between the given pair of v

Find the smallest positive angle between the given pair of vectors. (1,3) (5,2) Round to the nearest tenth.

Solution

angle between the vectors is given by

cos theta = u.v / ||u|| ||v||

u.v = 1*5 + 3*2 = 5 + 6

||u|| = sqrt (1^2 + 3^2 ) =sqrt 10

||v|| = sqrt (5^2 + 2^2 ) = sqrt 29

cos theta = 5 + 6 / sqrt 10 * sqrt 29

theta = 49.8 degrees