The position vector of a point C with respect to B is `hat i +hat j` and that of B with respect to A is `hati-hatj`. The position vector of C with respect to A is

Options

A. `2hati`
B. `2hatj`
C. `-2hatj`
D. `-2hati`

Explanation

To find the position vector of point C with respect to point A, we can use the relationship between the position vectors given in the question. Let's denote the vectors as follows:

- \( \vec{C} \) is the position vector of point C with respect to point B.
- \( \vec{B} \) is the position vector of point B with respect to point A.
- \( \vec{A} \) is the position vector of point C with respect to point A.

### Step-by-Step Solution:

1. **Identify the Given Vectors:**
- The position vector of C with respect to B is given as:
\[ \vec{C} = \hat{i} + \hat{j} \]
- The position vector of B with respect to A is given as:
\[ \vec{B} = \hat{i} - \hat{j} \]

2. **Use the Triangle Law of Vectors:**
According to the triangle law of vector addition, we have:
\[ \vec{A}C = \vec{A}B + \vec{B}C \]
This means:
\[ \vec{A}C = \vec{B} + \vec{C} \]

3. **Substitute the Known Vectors:**
Substitute the vectors we have:
\[ \vec{A}C = (\hat{i} - \hat{j}) + (\hat{i} + \hat{j}) \]

4. **Combine the Vectors:**
Now, combine the vectors:
\[ \vec{A}C = \hat{i} - \hat{j} + \hat{i} + \hat{j} \]
Simplifying this gives:
\[ \vec{A}C = 2\hat{i} \]

5. **Final Result:**
Therefore, the position vector of C with respect to A is:
\[ \vec{A}C = 2\hat{i} \]

### Conclusion:
The position vector of point C with respect to point A is \( 2\hat{i} \).