Question

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

Answer 1

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°.