Final answer:
The component form of the vector with a magnitude of 10 and a bearing angle of S40°E is found using trigonometric functions. The x-component is 10 × cos(40°) and the y-component is -10 × sin(40°), giving us the vector in component form: <7.66, -6.43>.
Step-by-step explanation:
To find the component form of the vector with a given magnitude and bearing angle, we can use trigonometric relationships. Since the vector has a magnitude of 10 and a bearing angle of S40°E, we first need to recognize that the bearing angle is measured from the south, going 40° towards the east. Therefore, in the Cartesian coordinate system, this vector will have a negative y-component (as it is going south) and a positive x-component (as it is going east).
Using the relationships Ax = A cos θ and Ay = A sin θ, we can find the horizontal and vertical components:
- Ax = 10 × cos(40°)
- Ay = 10 × sin(40°)
Note that we must use the negative sign for Ay since the vector is pointing south.
The exact component form of the vector can be calculated by inserting the cosine and sine values:
- Ax = 10 × (0.766) = 7.66
- Ay = -10 × (0.643) = -6.43
Therefore, the component form of the vector is <7.66, -6.43>.