Question

Determine the moment about the origin O of the force F=(13)i + (-12)j + 14(k) that acts at a point A. Assume that the position vector of A is r=2i+3j-4k. The moment about the origin of the force F is ()i+()j+()k

Answer 1

Answer:

$\vec{\tau} = 6\hat{i} + 80\hat{j}+63\hat{k}$

Explanation:

given,

F=(13)i + (-12)j + 14(k)

position vector  of vector A = r = 2 i + 3 j - 4 k

moment of force about origin

$\vec{\tau} = \vec{F} \times \vec{r}$

$\vec{\tau} = \begin{bmatrix}\hat{i} &\hat{j}&\hat{j} \\ 13 & -12 &14 \\2& 3 & -4\end{bmatrix}$

$\vec{\tau} = 6\hat{i} + 80\hat{j}+63\hat{k}$