The torque of a force `F = - 6 hat (i)` acting at a point `r = 4 hat(j)` about origin will be

Options

A. `-24 hat(k)`
B. `24 hat(k)`
C. `24 hat(j)`
D. `24 hat(i)`

Explanation

To find the torque \(\tau\) of a force \(\mathbf{F}\) acting at a point \(\mathbf{r}\) about the origin, we use the formula:

\[ \mathbf{\tau} = \mathbf{r} \times \mathbf{F} \]

### Step 1: Identify the vectors
Given:
- Force vector \(\mathbf{F} = -6 \hat{i}\)
- Position vector \(\mathbf{r} = 4 \hat{j}\)

### Step 2: Write the cross product
We need to calculate the cross product \(\mathbf{r} \times \mathbf{F}\):
\[ \mathbf{\tau} = \mathbf{r} \times \mathbf{F} = (4 \hat{j}) \times (-6 \hat{i}) \]

### Step 3: Apply the properties of cross product
Using the property of cross products, we know that:
\[ \hat{j} \times \hat{i} = -\hat{k} \]
Thus, we can rewrite the expression:
\[ \mathbf{\tau} = 4 \times (-6) \times (\hat{j} \times \hat{i}) = -24 (\hat{j} \times \hat{i}) = -24 (-\hat{k}) = 24 \hat{k} \]

### Step 4: Final result
So, the torque \(\mathbf{\tau}\) is:
\[ \mathbf{\tau} = 24 \hat{k} \]

### Conclusion
The correct answer is \(24 \hat{k}\).

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