Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 7>, v = <9, 7>

Solution:

The problem statement can be represented on the diagram as follows:

Vector u = (u₁, u₂) = (8,7)

Vector v = (v₁, v₂) = (9,7)

Θ = Cos⁻¹(u₁v₁ + u₂v₂)/IuI IvI

IuI = √(64 + 49) = √115

IvI = √(81 + 49) = √130

u₁v₁ =8 × 9 = 72

U₂v₂ = 7 × 7 = 49

Θ = Cos⁻¹(72 +49)/√115√130

= Cos⁻¹0.989612

= 0.144 radians or 8.3°

Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 7>, v = <9, 7>

Summary:

The angle between the two vectors as shown in the diagram is 8.3°.