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

Answer

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). Here, the first number (3) represents the x-coordinate, the second number (2) represents the y-coordinate, and the third number (5) represents the z-coordinate.

2. **Understand the Position Vector Representation**: In three-dimensional space, the position vector can be represented using unit vectors. The unit vectors are:
- \( \hat{i} \) for the x-axis,
- \( \hat{j} \) for the y-axis,
- \( \hat{k} \) for the z-axis.

3. **Construct the Position Vector**: The position vector \( \vec{r} \) can be constructed by multiplying each coordinate by its corresponding unit vector:
\[ \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} \]
Substituting the values:
\[ \vec{r} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k} \]

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