solve problem

Question

Find the angle between the given vectors 

 

a=i + j    b= 4i -3j

Answer 1

cos θ = (a · b) / (||a|| ||b||)

 

a = <1, 1>

||a|| = √2

 

b = <4, -3>

||b|| = 5

 

a · b = (1)(4) + (1)(-3)

a · b = 1

 

cos θ = 1 / 5√2

cos θ = √2 / 10

cos θ ≈ 1.4142 / 10

cos θ ≈ 0.14142

cos^-1 0.14142 ≈ 81.87°