Determine the angle (in degrees) between the vectors ⟨ 4 , − 5 ⟩ and ⟨ − 3 , − 2 ⟩ .

Answer 1

x=<4,-5>,y=<-3,-2>

x.y=4*(-3)+(-5)*(-2)=-12+10=-2

|x|=sqrt(4^2+(-5)^2)=sqrt(41)

|y|=sqrt((-3)^2+(-2)^2)=sqrt(13)

Let t be angle between them two vectors

cos(x)=x.y/(|x||y|)=-2/sqrt(41*13)=-2/sqrt(533)

x=arccos(-2/sqrt(533))