Position of a particle in a rectangular -co-ordinate `(3,2,5)`. Then its position vector will be

Options

A. `3hati+5hatj+2hatk`
B. `3hati+2hatj+5hatk`
C. `5hati+3hatj+2hatk`
D. none of these

Explanation

To find the position vector of a particle given its coordinates in a rectangular coordinate system, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates**:
The position of the particle is given as (3, 2, 5). This means:
- x-coordinate = 3
- y-coordinate = 2
- z-coordinate = 5

2. **Write the Position Vector**:
The position vector \( \vec{P} \) in a rectangular coordinate system can be expressed in terms of unit vectors \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \):
\[ \vec{P} = x \hat{i} + y \hat{j} + z \hat{k} \]

3. **Substitute the Coordinates**:
Now, substitute the values of the coordinates into the position vector formula:
\[ \vec{P} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]

4. **Final Expression**:
Therefore, the position vector of the particle is:
\[ \vec{P} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]

5. **Identify the Correct Option**:
From the options provided:
- Option 1: \( 3 \hat{i} + 5 \hat{j} + 2 \hat{k} \) (Incorrect)
- Option 2: \( 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \) (Correct)
- Option 3: \( 5 \hat{i} + 3 \hat{j} + 2 \hat{k} \) (Incorrect)
- Option 4: None of these (Incorrect)

The correct option is **Option 2**.