Question

Find the angle between the given vectors. Round your answer, in degrees, to two decimal places.u = (-5,6), v = (-5,-5)

Answer 1

For us to be able to determine the angle between vectors, we will be using the following formula:

$\text{ Cos }\Theta\text{ = }\frac{\text{ u }\cdot\text{ v}}{\lvert{\text{u}}\rvert\cdot\lvert{\text{v}}\rvert}$

Given:

u = (-5, 6)

v = (-5, -5)

We get,

u · v = u₁v₁ + u₂v₂ = (-5)(-5) + (6)(-5) = 25 - 30 = -5

|u| = √((-5)² + (6)²) = √(25 + 36) = √61

|v| = √((-5)² + (-5)²) = √(25 + 25) = √50 = 5√2

Let's now determine the angle of the two vectors,

$\text{ Cos }\Theta\text{ = }\frac{-5}{(\sqrt{61})(5\sqrt{2})}$$\text{ Cos }\Theta\text{ = -0.09053574604}$$\text{ }\Theta\text{ = Cos}^{-1}(−0.09053574604)$$\text{ }\Theta\text{ = 95.19442890773}\degree\text{ }\approx\text{ 95.19}\degree$

Therefore, the angle between the vectors is 95.19°