Al realizar el calculo de las operaciones con vectores en forma polar se obtiene:
A + B = (8.27, -5.2°)
B + C + D = (12.7; 1.08°)
A - D = (1.4; -45°)
D - B + A = (15.96; -72.68°)
La componentes polares de un vector se obtiene mediante:
- x: |u| Cos(α)
- y: |u| Sen(α)
U = [|u| Cos(α), |u| Sen(α)]
El módulo de un vector es: |u| = √(x² + y²)
A = (4i-5j)
|A| = √[4² + (-5)²]
|A| =√41
El ángulo es: α = Tan⁻¹(y/x)
sustituir;
α = Tan⁻¹(-5/4)
α = -51.34 + 360
α = 308.66°
A = (√41, 308.66°)
B = (6, 45°)
C = (4, 30°)
D = (-5i + 6j)
|D| = √[(-5)² + 6²]
|D| = √61
α = Tan⁻¹(6/-5)
α = -50.19 + 360
α = 309.8°
D = (√61, 309.8°)
Operaciones:
A + B = [√41 Cos(308.66°) + 6 Cos(45°); √41 Sen(308.66°) + 6 Sen(45°)]
A + B = [8.24; -0.75]
A + B = {√[(8.24)² + (-0.75)²],Tan⁻¹(-0.75/8.24)}
A + B = (8.27, -5.2°)
B + C + D = [6 Cos(45°) + 4 Cos(30°) + √61 Cos(309.8°); 6 Sen(45°) + 4 Sen(30°) + √61 Sen(309.8°)]
B + C + D = [12.7; 0.24]
B + C + D = {√[(12.7)² + (0.24)²],Tan⁻¹(0.24/12.7)}
B + C + D = (12.7; 1.08°)
A - D = [√41 Cos(308.66°) - √61 Cos(309.8°); √41 Sen(308.66°) - √61 Sen(309.8°)]
A - D = [-0.99; 1]
A - D = {√[(-0.99)² + (1)²],Tan⁻¹(1/-0.99)}
A - D = (1.4; -45°)
D - B + A = [√61 Cos(309.8°) - 6 Cos(45°) + √41 Cos(308.66°); 61 Sen(309.8°) - 6 Sen(45°) + √41 Sen(308.66°)]
D - B + A = [4.75; -15.24]
D - B + A = {√[4.75)² + (-15.24)²],Tan⁻¹(-15.24/4.75)}
D - B + A = (15.96; -72.68°)
