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The moment of the force \(\mathbf{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}\) acting at \((2,0,-3)\), about the point \((2,-2,-2)\), is given by

1. \(7\hat{i} - 8\hat{j} - 4\hat{k}\)
2. \(4\hat{i} - \hat{j} - 8\hat{k}\)
3. \(8\hat{i} - 4\hat{j} - 7\hat{k}\)
4. \(7\hat{i} - 4\hat{j} - 8\hat{k}\)

Correct answer: \(7\hat{i} - 4\hat{j} - 8\hat{k}\)

Solution

The moment about a point is \(\mathbf{r}\times\mathbf{F}\), where \(\mathbf{r}\) is the vector from the reference point to the point of application. Using \((2,0,-3)-(2,-2,-2)=(0,2,-1)\), the cross product with \((4,5,-6)\) gives the required moment.

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