A body constrained to move along y-axis is subjected to a constant force `vecF= -hati+2hatj+3hatk N`. The work done by this force in moving the body a distance of 4 m along y-axis is

Options

A. 4J
B. 8 J
C. 12J
D. 24 J

Explanation

To solve the problem of calculating the work done by the force \( \vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \) N when moving a body a distance of 4 m along the y-axis, we can follow these steps:

### Step 1: Identify the Force and the Displacement
The force acting on the body is given as:
\[ \vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \, \text{N} \]
The displacement along the y-axis is:
\[ \vec{d} = 0\hat{i} + 4\hat{j} + 0\hat{k} \, \text{m} \]

### Step 2: Calculate the Work Done
The work done \( W \) by a force when moving an object through a displacement is given by the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{d} \]
Calculating the dot product:
\[ W = (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (0\hat{i} + 4\hat{j} + 0\hat{k}) \]
This simplifies to:
\[ W = (-1 \cdot 0) + (2 \cdot 4) + (3 \cdot 0) = 0 + 8 + 0 = 8 \, \text{J} \]

### Step 3: Conclusion
The work done by the force in moving the body a distance of 4 m along the y-axis is:
\[ W = 8 \, \text{J} \]