How do you find the angle between u = <-1, 9> and v = <3, 12>?

Solution:

Given two vectors u = <-1, 9> and v = <3, 12>

u = -i + 9j; v = 3i + 12j

Using the dot product of the vectors, we know that cosθ = (u.v)/|u||v|

(u.v) = (-i + 9j ).(3i + 12j)

= (-1)(3) + (9)(12)

= -3 + 108

(u.v) = 105

|u| = √(1 + 81) = √82

|v| = √(9 + 144) = √153

Cosθ = 105/(√82 × √153) = 0.93

θ = cos^-1(0.93)

θ = 20.36°

How do you find the angle between u=<-1,9> and v=<3,12>?

Summary:

The angle between two vectors u = <-1, 9> and v = <3, 12> by using the cosθ formula is 20.36°.