Question

Vector u has a magnitude of 5 units and a direction angle of 75 degrees and vector v has a magnitude of 6 units and a direction angle 210 degrees. What is the component form of vector u+v?

Answer 1

To find the component form of vector u+v, we need to break down vector u and vector v into their respective horizontal and vertical components and then add them together.

Step-by-step explanation:

To find the component form of vector u+v, we need to break down vector u and vector v into their respective horizontal and vertical components. Given that vector u has a magnitude of 5 units and a direction angle of 75 degrees, we can find its horizontal component (ux) and vertical component (uy) using the following equations:

1. ux = 5 * cos(75°)
2. uy = 5 * sin(75°)

Similarly, for vector v with a magnitude of 6 units and a direction angle of 210 degrees, we can find its horizontal component (vx) and vertical component (vy) using the following equations:

1. vx = 6 * cos(210°)
2. vy = 6 * sin(210°)

Finally, to find the component form of vector u+v, we add the corresponding horizontal components together and the corresponding vertical components together. The component form (ux+vx, uy+vy) represents the resultant vector.