`hat(i)` and `hat(j)` are unit vectors along x-and y-axes respectively. What is the magnitude and the direction of the vectors `hat(i)+hat(j)` and `hat(i)-hat(j)`? What are the components of a vector `vec(A)=2hat(i)+3hat(j)` along the direction `hat(i)+hat(j)`and `hat(i)-hat(j)`?

Explanation

To solve the problem step by step, we will break it down into parts: finding the magnitude and direction of the vectors \( \hat{i} + \hat{j} \) and \( \hat{i} - \hat{j} \), and then finding the components of the vector \( \vec{A} = 2\hat{i} + 3\hat{j} \) along these two directions.

### Step 1: Find the Magnitude and Direction of \( \hat{i} + \hat{j} \)

1. **Magnitude Calculation**:
\[ \text{Magnitude} = |\hat{i} + \hat{j}| = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2} \]
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