If `hatn` is the unit vector in the direction of `vecA` then `hatn` is equal to

Options

A. `vec A xx A`
B. `n xx A`
C. `(vec A)/(A)`
D. `(A)/(vec A)`

Explanation

To find the unit vector \( \hat{n} \) in the direction of the vector \( \vec{A} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of a Unit Vector**:
A unit vector is a vector that has a magnitude of 1. It is obtained by dividing a vector by its magnitude.

2. **Express the Vector \( \vec{A} \)**:
Let \( \vec{A} \) be expressed in terms of its components:
\[ \vec{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k} \]
where \( A_x, A_y, \) and \( A_z \) are the components of the vector in the x, y, and z directions respectively.

3. **Calculate the Magnitude of \( \vec{A} \)**:
The magnitude \( A \) of the vector \( \vec{A} \) is given by:
\[ A = \sqrt{A_x^2 + A_y^2 + A_z^2} \]

4. **Find the Unit Vector \( \hat{n} \)**:
The unit vector \( \hat{n} \) in the direction of \( \vec{A} \) can be calculated as:
\[ \hat{n} = \frac{\vec{A}}{|\vec{A}|} = \frac{A_x \hat{i} + A_y \hat{j} + A_z \hat{k}}{\sqrt{A_x^2 + A_y^2 + A_z^2}} \]

5. **Final Expression**:
Thus, the unit vector \( \hat{n} \) is given by:
\[ \hat{n} = \frac{A_x}{A} \hat{i} + \frac{A_y}{A} \hat{j} + \frac{A_z}{A} \hat{k} \]
where \( A \) is the magnitude of \( \vec{A} \).

### Conclusion:
The unit vector \( \hat{n} \) in the direction of \( \vec{A} \) is equal to \( \frac{\vec{A}}{|\vec{A}|} \).