Question

Determine the moment vector m about the origin, o, of a force f= 10i-j+2k passing through the point with position vector r=2i-3j+5k

Answer 1

$$\vec M=\vec {r}\times\vec{F}=\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 2 & -3 & 5 \\ 10 & -1 & 2 \\ \end{vmatrix}$$

$$=\vec{i}\begin{vmatrix} -3 & 5 \\ -1 & 2 \end{vmatrix}-\vec{j}\begin{vmatrix} 2 & 5 \\ 10 & 2 \end{vmatrix}+\vec{k}\begin{vmatrix} 2 & -3 \\ 10 & -1 \end{vmatrix}$$

$$=-\vec{i}+46\vec{j}+28\vec{k}$$