Find the angle (θ) between the vectors. Round your answer to the nearest tenth.

Question

u = 2i - 3j

v = i - 2j

θ = __ ?______ Degrees

Answer 1

cosθ = [u • v]/ [ llull llvll ]

 

u = 2i - 3j     v = i - 2j

 

u • v = (2)(1) + (-3)(-2) = 8

 

llull = √[2² + (-3)²] = √13    llvll = √[1² + (-2)²] = √5

 

So, cosθ = 8 / [√13 √5] = 8 / √65

 

          θ = Arccos(8 / √65) ≈ 7.1°