Find the angle between the pair of vector to the nearest tenth of degree (4,5), (-4,-1)

Step-by-step explanation:

Given the pair vector

U = (4, 5) = 4•i + 5•j

V = (-4, - 1) = - 4•i - 1•j

Then,

The angle between two vectors can be determined using

U•V = |U||V| Cosθ

|U| = √ (4²+5²) = √ (16 + 25) = √41

|V| = √ (-4) ² + (-1) ² = √ (16 + 1) = √17

U•V = |U||V| Cosθ

(4•i + 5•j) • (-4•i - 1•j) = √41 * √17 Cosθ

-16 - 5 = √ (41*17) Cosθ

-21 = √697 Cosθ

Cosθ = - 21 / √697

Cosθ = - 0.7954

θ = Arccos (-0.7954)

θ = 142.7°.