Four vectors start at the origin of the x y axes labeled O. Vector A is directed along the negative y axis and has a length of 8.00 meters. Vector B is located in the first quadrant, it makes an angle of 30.0 degrees with the positive y axis and has a length of 15.0 meters. Vector C is located in the third quadrant, it makes an angle of 25.0 degrees with the negative x axis and has a length of 12.0 meters. Vector D is located in the second quadrant, it makes an angle of 53.0 degrees with the negative x axis and has a length of 10.0 meters. - Four vectors starting at the origin

Compute the x- and y-components of the vectors A⃗, B⃗, C⃗, and D⃗ in (Figure 1).

Express your answer in meters.

To find the \( x \)- and \( y \)-components of the vectors \( \mathbf{A} \), \( \mathbf{B} \), \( \mathbf{C} \), and \( \mathbf{D} \), we'll use trigonometry. Each vector can be decomposed into its components using the following formulas:

- \( x \)-component: \( \text{Magnitude} \times \cos(\text{Angle}) \)
- \( y \)-component: \( \text{Magnitude} \times \sin(\text{Angle}) \)

Let's go through each vector one by one.

### 1. **Vector \( \mathbf{A} \)**
- **Direction**: Along the negative \( y \)-axis.
- **Magnitude**: 8.00 meters.

Since \( \mathbf{A} \) is directed entirely along the negative \( y \)-axis:
- \( A_x = 0 \) meters
- \( A_y = -8.00 \) meters

### 2. **Vector \( \mathbf{B} \)**
- **Direction**: Located in

Learn how to compute the x and y components of vectors A, B, C, and D starting from the origin. This problem involves trigonometric calculations to determine vector components based on magnitude and direction angles. Suitable for high school students studying vector analysis.

Math Problem Statement

Solution

1. Vector $\mathbf{A}$

2. Vector $\mathbf{B}$

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