Answer:
R = (- 3.72î + 8.29j)
Magnitude of R = 9.09 m
Explanation:
Let î and j represent unit vectors along the x and y axis respectively.
Vector A --> magnitude 8.78 m, direction 37.0° from the +x-axis
Let the x and y components of this vector be Aₓ and Aᵧ
A = (Aₓî + Aᵧj) m
The components given magnitude and direction from the +x-axis are calculated as
Aₓ = A cos θ and Aᵧ = A sin θ
Aₓ = (8.78 cos 37°) = 7.01 m
Aᵧ = (8.78 sin 37°) = 5.28 m
A = (7.01î + 5.28j) m
Vector B has magnitude 8.26 m and direction 135° from the +x-axis
B = (Bₓî + Bᵧj) m
Bₓ = (8.26 cos 135°) = - 5.84 m
Bᵧ = (8.26 sin 135°) = 5.84 m
B = (-5.84î + 5.84j) m
Vector C has magnitude 5.65 m and direction 210° from the +x-axis
C = (Cₓî + Cᵧj) m
Cₓ = (5.65 cos 210°) = - 4.89 m
Cᵧ = (5.65 sin 210°) = - 2.83 m
C = (- 4.89î - 2.83j) m
The resultant force is a vector sum of all the forces. Let the resultant force be R
R = (Rₓî + Rᵧj) m
R = A + B + C = (7.01î + 5.28j) + (-5.84î + 5.84j) + (- 4.89î - 2.83j)
Summing the î and j components seperately,
R = (- 3.72î + 8.29j) m
To get its magnitude,
Magnitude of R = √(Rₓ² + Rᵧ²) = √((-3.72)² + (8.29)²) = 9.09 m
= characteristic wavelength = 9 μm = 9 x 10⁻⁹ m