Final answer:
To find the sum of two vectors, we resolve each into its horizontal and vertical components, add these components, and use trigonometry to find the magnitude and direction of the resultant vector.
Step-by-step explanation:
To find the sum of the vectors A and B with angles given as 30°, we first need to resolve each vector into its horizontal (x) and vertical (y) components. Once we have the components, we can add the horizontal components and the vertical components of the vectors separately to find the resultant vector R.
For the vector A at a 30° angle and vector B at a -110° angle:
- Resolve vector A into its components: Ax = A × cos(30°), Ay = A × sin(30°)
- Resolve vector B into its components: Bx = B × cos(-110°), By = B × sin(-110°)
- Add the components to get R: Rx = Ax + Bx, Ry = Ay + By
- Determine the magnitude and direction of R using trigonometry
For the other parts of the question such as vector S = A - 3B + C and D = A - B, we would follow a similar process. For vector -3B, we multiply the components of B by -3 before adding them to the components of A and C.
In the case presented as an example, after determining the components for each vector, we could construct vector S by drawing vectors A, -3B, and C tail-to-head and then measuring the resultant vector S with a ruler and protractor to find that its magnitude is S = 36.9 cm with a direction angle of 52.9°.