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

Options

A. `3hat(i) + 5hat(j) + 2hat(k)`
B. `3hat(i) + 2hat(j) + 5hat(k)`
C. `5hat(i) + 3hat(j) + 2hat(k)`
D. none of these

Answer

To find the position vector of a particle located at the coordinates (3, 2, 5) in a rectangular coordinate system, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates**:
The given coordinates of the particle are (3, 2, 5). Here, 3 is the x-coordinate, 2 is the y-coordinate, and 5 is the z-coordinate.

2. **Understand the Position Vector**:
The position vector of a point in three-dimensional space is represented as a vector that points from the origin (0, 0, 0) to the point (x, y, z).

3. **Express the Coordinates in Vector Form**:
In vector form, the position vector can be expressed using unit vectors:
- The x-component (3) is represented by \(3 \hat{i}\),
- The y-component (2) is represented by \(2 \hat{j}\),
- The z-component (5) is represented by \(5 \hat{k}\).

Therefore, the position vector \( \vec{P} \) can be written as:
\[ \vec{P} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]

4. **Combine the Components**:
The final position vector is the sum of the individual components:
\[ \vec{P} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]

5. **Conclusion**:
Thus, the position vector of the particle located at (3, 2, 5) is:
\[ \vec{P} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]