The magnitude of ` hati + hatj` is

Options

A. 2
B. 0
C. `sqrt2`
D. 4

Answer

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

### Step-by-Step Solution:

1. **Identify the Vector Components**:
The vector given is \( \hat{i} + \hat{j} \). Here, \( \hat{i} \) represents the unit vector in the x-direction and \( \hat{j} \) represents the unit vector in the y-direction.

2. **Write the Magnitude Formula**:
The magnitude \( | \vec{A} | \) of a vector \( \vec{A} = a \hat{i} + b \hat{j} \) is given by the formula:
\[ | \vec{A} | = \sqrt{a^2 + b^2} \]
where \( a \) and \( b \) are the coefficients of \( \hat{i} \) and \( \hat{j} \) respectively.

3. **Substitute the Values**:
For the vector \( \hat{i} + \hat{j} \), the coefficients are:
- \( a = 1 \) (coefficient of \( \hat{i} \))
- \( b = 1 \) (coefficient of \( \hat{j} \))

Substituting these values into the magnitude formula:
\[ | \hat{i} + \hat{j} | = \sqrt{1^2 + 1^2} \]

4. **Calculate the Magnitude**:
\[ | \hat{i} + \hat{j} | = \sqrt{1 + 1} = \sqrt{2} \]

5. **Final Result**:
The magnitude of the vector \( \hat{i} + \hat{j} \) is \( \sqrt{2} \).

### Summary:
Thus, the magnitude of \( \hat{i} + \hat{j} \) is \( \sqrt{2} \).

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