The unit vector along `hati+hatj` is

Options

A. `hatk`
B. `hati+hathatj`
C. `(hati+hatj)/(sqrt(2))`
D. `(hati+hatj)/(2)`

Explanation

To find the unit vector along the vector \( \hat{i} + \hat{j} \), we can follow these steps:

### Step 1: Define the vector
Let the vector \( \mathbf{A} \) be defined as:
\[ \mathbf{A} = \hat{i} + \hat{j} \]

### Step 2: Calculate the magnitude of the vector
The magnitude of vector \( \mathbf{A} \) is calculated using the formula:
\[ |\mathbf{A}| = \sqrt{(1^2 + 1^2)} = \sqrt{1 + 1} = \sqrt{2} \]

### Step 3: Find the unit vector
The unit vector \( \hat{u} \) in the direction of vector \( \mathbf{A} \) is given by:
\[ \hat{u} = \frac{\mathbf{A}}{|\mathbf{A}|} \]
Substituting the values we have:
\[ \hat{u} = \frac{\hat{i} + \hat{j}}{\sqrt{2}} \]

### Step 4: Write the final answer
Thus, the unit vector along \( \hat{i} + \hat{j} \) is:
\[ \hat{u} = \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \]

### Conclusion
The unit vector along \( \hat{i} + \hat{j} \) is \( \frac{1}{\sqrt{2}} (\hat{i} + \hat{j}) \).

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