Given the vectors u langle 2 4 rangle and v langle 11 1 r

Given the vectors u = langle 2, -4 rangle and v = langle 11, - 1 rangle, find the angle between the two vectors. 51.6 degree 58.2 degree 22.3 degree 89.1 degree

Solution

cos theta = u*v/(magnitude of u * magnitude of v)

u.v= 2*11 +(-4)(-1)=22+4=26

magnitude of u= sqrt(2)^2 +(-4)^2=sqrt(20)

magnitude of v= sqrt(11^2 +(-1)^2)=sqrt122

therefore cos theta= 26/(sqrt(20*122))=26/sqrt2440

theta=58.2 degree