Find `vec a +vec b` if `vec a = hat i - hat j` and `vec b =2 hat i`

Answer

To find the sum of the vectors \( \vec{a} \) and \( \vec{b} \), we will follow these steps:

1. **Identify the given vectors**:
- \( \vec{a} = \hat{i} - \hat{j} \)
- \( \vec{b} = 2\hat{i} \)

2. **Express the vectors in component form**:
- \( \vec{a} = 1\hat{i} + (-1)\hat{j} + 0\hat{k} \) (since there is no \( \hat{k} \) component)
- \( \vec{b} = 2\hat{i} + 0\hat{j} + 0\hat{k} \)

3. **Add the vectors component-wise**:
- For the \( \hat{i} \) component: \( 1 + 2 = 3 \)
- For the \( \hat{j} \) component: \( -1 + 0 = -1 \)
- For the \( \hat{k} \) component: \( 0 + 0 = 0 \)

4. **Combine the results**:
- Thus, \( \vec{a} + \vec{b} = 3\hat{i} - 1\hat{j} + 0\hat{k} \)

5. **Simplify the expression**:
- Since the \( \hat{k} \) component is zero, we can write the final result as:
- \( \vec{a} + \vec{b} = 3\hat{i} - \hat{j} \)

### Final Answer:
\[ \vec{a} + \vec{b} = 3\hat{i} - \hat{j} \]