Final answer:
To find the sum of three vectors, determine their components along a chosen set of axes using trigonometric functions, then add these components along each axis and finally apply the Pythagorean theorem to calculate the resultant's magnitude.
Step-by-step explanation:
To determine the components of the sum of three vectors, follow these steps:
- Identify the x- and y-axes that will be used in the problem.
- Find the components of each vector to be added along the chosen perpendicular axes using the equations Ax = A cos θ and Ay = A sin θ for vector A, and similarly for vectors B and C.
- Add the components of the individual vectors along the same axis to find the components of the resultant vector. For example, the x-component of the resultant (Rx) would be computed as Rx = Ax + Bx + Cx.
- To get the magnitude R of the resultant vector, use the Pythagorean theorem, considering that there might be a typographical error in the provided material. The correct formula should involve both x and y components: R = √(Rx2 + Ry2).
This process will allow you to determine the sum of the vectors' x and y components, from which you can then find the magnitude and direction of the resultant vector.