It looks like you're working on a vector addition problem, where two displacements (A and B) are given. From the diagram, you're asked to find the resultant vector R, which is the sum of these two displacements. You also need to determine the magnitude and direction of the resulting displacement.

To solve this problem analytically:

1. Break down the displacements into components:

   • Displacement A is along the x-axis (west direction).
   • Displacement B is at an angle θ (to the north-east).

   We can decompose both displacements into their x and y components:

   • For A:
     $A_x = A$ (since it lies on the x-axis)
     $A_y = 0$ (there is no displacement in the y-direction for A)

   • For B:
     $B_x = B \cdot \cos(\theta)$
     $B_y = B \cdot \sin(\theta)$

2. Add the components to find the resultant vector's components: The total displacement components are:

   • $R_x = A_x + B_x = A + B \cdot \cos(\theta)$
   • $R_y = A_y + B_y = B \cdot \sin(\theta)$

3. Find the magnitude of the resultant vector R: $R = \sqrt{R_x^2 + R_y^2}$

4. Find the direction (angle θ) of the resultant vector: $\theta = \tan^{-1}\left(\frac{R_y}{R_x}\right)$

You need to plug in the values for A, B, and θ to compute the final answer. If you have those values, I can help you compute them.

Would you like to go over this in more detail, or do you have the specific values for A, B, and θ that we can use?