Forces of `1` and `2 units` act along the lines `x = 0` and ` y = 0`. The equation of the line of action of the resultant is

Options

A. `y - 2 x = 0`
B. `2y - x = 0`
C. `y + x = 0`
D. `y - x = 0`

Explanation

To solve the problem step by step, we will analyze the forces acting along the lines \(x = 0\) and \(y = 0\) and find the equation of the line of action of the resultant force.

### Step 1: Identify the Forces
We have two forces:
- A force of \(1\) unit acting along the line \(x = 0\) (the y-axis).
- A force of \(2\) units acting along the line \(y = 0\) (the x-axis).

### Step 2: Represent the Forces as Vectors
The forces can be represented as vectors:
- The force of \(1\) unit along the y-axis can be represented as \(\vec{F_1} = (0, 1)\).
- The force of \(2\) units along the x-axis can be represented as \(\vec{F_2} = (2, 0)\).

### Step 3: Determine the Resultant Force
The resultant force \(\vec{R}\) can be found by vector addition:
\[ \vec{R} = \vec{F_1} + \vec{F_2} = (0, 1) + (2, 0) = (2, 1) \]

### Step 4: Find the Slope of the Resultant Force
The coordinates of the resultant force are \((2, 1)\). To find the slope \(m\) of the line of action of the resultant, we use the formula:
\[ m = \frac{\Delta y}{\Delta x} = \frac{1 - 0}{2 - 0} = \frac{1}{2} \]

### Step 5: Write the Equation of the Line
Since the line passes through the origin \((0, 0)\) and has a slope of \(\frac{1}{2}\), we can use the point-slope form of the equation of a line:
\[ y = mx \implies y = \frac{1}{2}x \]

### Step 6: Rearranging the Equation
To express this in standard form, we can rearrange the equation:
\[ 2y = x \implies 2y - x = 0 \]

### Conclusion
The equation of the line of action of the resultant force is:
\[ 2y - x = 0 \]