Find the projection of the vector ` hat i- hat j`on the vector ` hat i+ hat j`

Explanation

To find the projection of the vector \( \hat{i} - \hat{j} \) on the vector \( \hat{i} + \hat{j} \), we can use the formula for the projection of vector \( \mathbf{a} \) onto vector \( \mathbf{b} \):

\[ \text{proj}_{\mathbf{b}} \mathbf{a} = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{b}|^2} \mathbf{b} \]

### Step 1: Identify the vectors
Let:
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