b) Analytical MethodVectors X - component Y - componentA = 220 km, 10 0 N of W A X = A Y =B = 250 km, 45 0 W of N B X = B Y =C = 200 km, 50 0 N of E C X = C Y =D = 300 KM, 80 0 E of S D X = D Y =R X = R Y

The given problem involves vector analysis. We are given four vectors A, B, C, and D with their magnitudes and directions. We are asked to find their X and Y components.

The X and Y components of a vector can be found using the equations:

X = rcos(θ) Y = rsin(θ)

where r is the magnitude of the vector and θ is the angle it makes with the reference direction.

1. Vector A = 220 km, 10° N of W This means the vector is 10° north from the west direction. In terms of standard angles, this is equivalent to 180° - 10° = 170°.

A_X = 220cos(170°) A_Y = 220sin(170°)

2. Vector B = 250 km, 45° W of N This means the vector is 45° west from the north direction. In terms of standard angles, this is equivalent to 90° - 45° = 45°.

B_X = 250cos(45°) B_Y = 250sin(45°)

3. Vector C = 200 km, 50° N of E This means the vector is 50° north from the east direction. In terms of standard angles, this is equivalent to 0° + 50° = 50°.

C_X = 200cos(50°) C_Y = 200sin(50°)

4. Vector D = 300 km, 80° E of S This means the vector is 80° east from the south direction. In terms of standard angles, this is equivalent to 270° - 80° = 190°.

D_X = 300cos(190°) D_Y = 300sin(190°)

Finally, the X and Y components of the resultant vector R can be found by adding the X and Y components of all the vectors.

R_X = A_X + B_X + C_X + D_X R_Y = A_Y + B_Y + C_Y + D_Y

Please note that the actual numerical values will depend on the units of the angles (whether they are in degrees or radians) and the trigonometric functions used (whether they are for degrees or radians).