Three ships A, B and C are in motion. The motion of A as seen by B is with speed v towards north-east . The motion. Of B as seen by C is with speed v towards the north-west. Then as seen by A, C will be moving towards

Options

A. north
B. south
C. east
D. west

Explanation

To solve the problem step by step, we will analyze the motion of ships A, B, and C based on the given information.

### Step 1: Understand the motion of A as seen by B
- The problem states that the motion of ship A as seen by ship B is towards the northeast with speed v.
- In vector terms, the northeast direction can be represented as a combination of the north and east components. Therefore, the velocity of A with respect to B can be expressed as:
\[ \vec{V}_{A/B} = v \left( \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \right) \]
where \(\hat{i}\) is the east direction and \(\hat{j}\) is the north direction.

### Step 2: Understand the motion of B as seen by C
- The motion of ship B as seen by ship C is towards the northwest with speed v.
- The northwest direction can similarly be represented as:
\[ \vec{V}_{B/C} = v \left( -\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \right) \]

### Step 3: Express velocities in terms of components
- From the above, we can express the velocities of A and B in terms of their components:
- For A with respect to B:
\[ \vec{V}_{A} = \vec{V}_{B} + \vec{V}_{A/B} \]
- For B with respect to C:
\[ \vec{V}_{B} = \vec{V}_{C} + \vec{V}_{B/C} \]

### Step 4: Calculate the relative velocity of C with respect to A
- To find the velocity of C as seen by A, we need to calculate:
\[ \vec{V}_{C/A} = \vec{V}_{C} - \vec{V}_{A} \]
- Rearranging gives:
\[ \vec{V}_{C/A} = \vec{V}_{C} - (\vec{V}_{B} + \vec{V}_{A/B}) \]

### Step 5: Substitute the expressions
- Substitute the expressions for \(\vec{V}_{B}\) and \(\vec{V}_{A/B}\):
\[ \vec{V}_{C/A} = \vec{V}_{C} - \left( \vec{V}_{C} + \vec{V}_{B/C} + \vec{V}_{A/B} \right) \]
- This simplifies to:
\[ \vec{V}_{C/A} = -\vec{V}_{B/C} - \vec{V}_{A/B} \]

### Step 6: Analyze the direction of C as seen by A
- Now, we need to analyze the resultant vector \(\vec{V}_{C/A}\). The components of \(\vec{V}_{B/C}\) and \(\vec{V}_{A/B}\) will determine the direction.
- The velocity of C relative to A will have components that can be calculated based on the directions of A and B.

### Conclusion
- After analyzing the components and directions, we find that the resultant velocity of C as seen by A will point towards the south direction.

### Final Answer
- Therefore, as seen by A, C will be moving towards the **south**.