Final answer:
To determine the position vector of A at a bearing of 120°, convert the bearing to an angle from the positive x-axis, then calculate the components using cosine and sine functions. The position vector of A is 8 units away from the origin and will have components of (-4, -6.928).
Step-by-step explanation:
To find the position vector of A if it is 8 units away from the origin at a bearing of 120°, we need to use trigonometry to break down the vector into its x and y components. A bearing of 120° indicates that the angle measured clockwise from the north direction is 120°. However, in vector calculations, angles are typically measured counterclockwise from the positive x-axis (east direction). This means we need to convert the bearing to this standard convention.
Since north corresponds to the positive y-axis, a bearing of 120° is equivalent to an angle of 180° + (180° - 120°) = 240° when measured counter-clockwise from the positive x-axis. We can now calculate the components:
- X component (Ax) = Magnitude × cos(angle) = 8 × cos (240°)
- Y component (Ay) = Magnitude × sin(angle) = 8 × sin (240°)
Calculating these components using a calculator set to degree mode:
- Ax = 8 × cos (240°) = 8 × (-0.5) = -4 units
- Ay = 8 × sin (240°) = 8 × (-0.8660) = -6.928 units
The position vector of A is thus (-4, -6.928).