The unit vector along `vec(i)+vec(j)` is :-

Options

A. `vec(k)`
B. `hat(i)+hat(j)`
C. `(hat(i)+hat(j))/(sqrt(2))`
D. `(hat(i)+hat(j))/(2)`

Explanation

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

### Step 1: Identify the vector
The vector we are dealing with is:
\[ \vec{A} = \vec{i} + \vec{j} \]

### Step 2: Calculate the magnitude of the vector
The magnitude of a vector \(\vec{A} = \vec{i} + \vec{j}\) can be calculated using the formula:
\[ |\vec{A}| = \sqrt{(A_x)^2 + (A_y)^2} \]
Here, \(A_x = 1\) (coefficient of \(\vec{i}\)) and \(A_y = 1\) (coefficient of \(\vec{j}\)). Therefore, the magnitude is:
\[ |\vec{A}| = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2} \]

### Step 3: Calculate the unit vector
The unit vector \(\hat{A}\) in the direction of \(\vec{A}\) is given by:
\[ \hat{A} = \frac{\vec{A}}{|\vec{A}|} \]
Substituting \(\vec{A}\) and its magnitude:
\[ \hat{A} = \frac{\vec{i} + \vec{j}}{\sqrt{2}} \]

### Final Answer
Thus, the unit vector along \(\vec{i} + \vec{j}\) is:
\[ \hat{A} = \frac{1}{\sqrt{2}} \vec{i} + \frac{1}{\sqrt{2}} \vec{j} \]