Two forces `f_(1)=4N` and `f_(2)=3N` are acting on a particle along positve `X-`axis and negative `y-`axis respectively. The resultant force on the particle will be`-`

Options

A. `3hat(i)+4hat(j)`
B. `4hat(i)+3hat(j)`
C. `4hat(i)-3hat(j)`
D. `3hat(i)-4hat(j)`

Explanation

To find the resultant force acting on the particle due to the two forces \( F_1 \) and \( F_2 \), we can follow these steps:

### Step 1: Identify the forces and their directions
- The first force \( F_1 = 4 \, \text{N} \) is acting along the positive x-axis.
- The second force \( F_2 = 3 \, \text{N} \) is acting along the negative y-axis.

### Step 2: Represent the forces as vectors
- The force \( F_1 \) can be represented as a vector:
\[ \mathbf{F_1} = 4 \, \hat{i} \]
- The force \( F_2 \) can be represented as a vector:
\[ \mathbf{F_2} = -3 \, \hat{j} \]

### Step 3: Calculate the resultant force
- The resultant force \( \mathbf{F_R} \) is the vector sum of \( \mathbf{F_1} \) and \( \mathbf{F_2} \):
\[ \mathbf{F_R} = \mathbf{F_1} + \mathbf{F_2} = 4 \, \hat{i} + (-3 \, \hat{j}) = 4 \, \hat{i} - 3 \, \hat{j} \]

### Step 4: Write the final expression for the resultant force
- Therefore, the resultant force acting on the particle is:
\[ \mathbf{F_R} = 4 \, \hat{i} - 3 \, \hat{j} \]