To find the x- and y-components of each vector, we can use trigonometry. Let's break down each vector into its components:

Vector A⃗:

• Given: Vector A is directed along the negative y-axis and has a length of 8.00 meters.
• Components:
  • $A_x = 0$ (since it lies along the y-axis, there's no x-component)
  • $A_y = -8.00 \, \text{m}$ (since it points in the negative y direction)

Vector B⃗:

• Given: Vector B is located in the first quadrant, makes an angle of 30.0 degrees with the positive y-axis, and has a length of 15.0 meters.
• Components:
  • The angle with the positive x-axis: $\theta_B = 90^\circ - 30^\circ = 60^\circ$
  • $B_x = 15.0 \, \text{m} \times \cos(60^\circ)$
  • $B_y = 15.0 \, \text{m} \times \sin(60^\circ)$

Vector C⃗:

• Given: Vector C is located in the third quadrant, makes an angle of 25.0 degrees with the negative x-axis, and has a length of 12.0 meters.
• Components:
  • The angle with the negative x-axis is $25^\circ$.
  • The angle with the positive x-axis: $\theta_C = 180^\circ + 25^\circ = 205^\circ$
  • $C_x = 12.0 \, \text{m} \times \cos(205^\circ)$
  • $C_y = 12.0 \, \text{m} \times \sin(205^\circ)$

Vector D⃗:

• Given: Vector D is located in the second quadrant, makes an angle of 53.0 degrees with the negative x-axis, and has a length of 10.0 meters.
• Components:
  • The angle with the positive x-axis: $\theta_D = 180^\circ - 53^\circ = 127^\circ$
  • $D_x = 10.0 \, \text{m} \times \cos(127^\circ)$
  • $D_y = 10.0 \, \text{m} \times \sin(127^\circ)$

Now, let's compute the components:

Computation:

• ( B