If ` vecA+vecB` is a unit vector along x-axis and `vecA = hati-hatj+hatk`, then what is `vecB` ?

Options

A. `hati+hatk`
B. `hatj-hatk`
C. `hati+hatj+hatk`
D. `hati+hatj-hatk`

Explanation

To solve the problem, we need to find the vector **B** given that **A + B** is a unit vector along the x-axis and **A** is defined as **A = i - j + k**.

### Step-by-Step Solution:

1. **Understand the given information**:
- We know that **A + B** is a unit vector along the x-axis. The unit vector along the x-axis is represented as **i**.
- We are given **A = i - j + k**.

2. **Set up the equation**:
- From the information provided, we can write:
\[ A + B = i \]

3. **Substitute the value of A**:
- Substitute **A** into the equation:
\[ (i - j + k) + B = i \]

4. **Rearranging the equation**:
- To isolate **B**, we can rearrange the equation:
\[ B = i - (i - j + k) \]

5. **Simplify the expression**:
- Distributing the negative sign:
\[ B = i - i + j - k \]
- This simplifies to:
\[ B = 0 + j - k \]
- Therefore, we have:
\[ B = j - k \]

6. **Final Result**:
- The vector **B** is:
\[ \vec{B} = j - k \]

### Conclusion:
The final answer is:
\[ \vec{B} = \hat{j} - \hat{k} \]