The expression `(1/(sqrt(2))hat(i)+1/(sqrt(2))hat(j))` is a

Options

A. Unit vector
B. Null vector
C. Vector of magnitude sqrt(2)`
D. Scalar

Explanation

To determine the nature of the expression \( \left( \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \right) \), we need to analyze its magnitude and compare it with the definitions of different types of vectors.

### Step-by-Step Solution:

1. **Identify the Vector Components**:
The given vector can be expressed as:
\[ \vec{A} = \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \]
Here, the components along the x-axis (i-direction) and y-axis (j-direction) are both \( \frac{1}{\sqrt{2}} \).

2. **Calculate the Magnitude of the Vector**:
The magnitude of a vector \( \vec{A} = a \hat{i} + b \hat{j} \) is given by the formula:
\[ |\vec{A}| = \sqrt{a^2 + b^2} \]
For our vector:
\[ |\vec{A}| = \sqrt{\left(\frac{1}{\sqrt{2}}\right)^2 + \left(\frac{1}{\sqrt{2}}\right)^2} \]
Simplifying this:
\[ |\vec{A}| = \sqrt{\frac{1}{2} + \frac{1}{2}} = \sqrt{1} = 1 \]

3. **Determine the Nature of the Vector**:
- A **unit vector** is defined as a vector with a magnitude of 1.
- A **null vector** (or zero vector) has a magnitude of 0.

Since we calculated the magnitude of \( \vec{A} \) to be 1, we can conclude that:
\[ \vec{A} \text{ is a unit vector.} \]

### Conclusion:
The expression \( \left( \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} \right) \) is a **unit vector**.