The resultant magnitude and direction of the vectors are as follows:
- A. A = 6.6; θ = 30.8° from the x-axis
- B. B = 10.4; θ = 196.7° from the x-axis
- C. C = 23.3; θ = 300° from the x-axis
- D. D = 40.4; θ = 138° from the x-axis
- E. E = 49.5; θ = 346° from the x-axis
What is the resultant magnitude and direction of the given vectors?
The resultant magnitude and direction of the vectors are as follows:
A. A = √(5.7² + 3.4²)
A = 6.6
θ = tan⁻¹(3.4/5.7)
θ = 30.8° from the x-axis
B. B = √{(-10)² + (-3²)}
B 10.4
θ = tan⁻¹(3/10) + 180
θ = 16.7° + 180°
θ = 196.7° from the x-axis
C. C = √{(12)² + (-20²)}
C = 23.3
θ = 360° - tan⁻¹(20/12)
θ = 300° from the x-axis
D. D = √{(-30)² + (27²)}
D = 40.4
θ = 180 - tan⁻¹(27/30)
θ = 138° from the x-axis
E. E = √{(48)² + (12²)}
E = 49.5
θ = 360° - tan⁻¹(12/48)
θ = 346° from the x-axis
In conclusion, the resultant of the vectors and direction are obtained using the resultant vector formula.
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