(i) Moment of force about origin

(ii) Moment of force about point B(2,1,2)m..

Given :- $\vec F=3i-4j+12k \\ \vec{r_A }=i-2j+3k \\ \vec{r_B }=2i+j+2k $

To find:-

$\vec{M_o },\vec{M_B }$

Solutions:

$\vec{M_o}=\vec{r_A} × \vec F$

$$=\begin{vmatrix} i&j&k\\ 1&-2&3\\ 3&-4&12 \end{vmatrix}$$

$ =(-24+12)i-(12-9)j+(-4+6)k \\ \therefore \vec{M_o}=-12i-3j+2k \space \space \space N-m \\ \vec{r_{AB}}=\vec{r_A}-\vec{r_B } \\ =(i-2j+3k)-(2i+j+2k) \\ \vec{r_{AB}}=-i-3j+k \\ \vec{M_B}=\vec{r_{AB}} × \vec F$

$$=\begin{vmatrix} i & j &k\\ -1 & -3& 1\\ 3 & -4& 12\end{vmatrix}$$

$ =(-36+4)i-(-12-3)j+(4+9)k \\ \therefore \vec{M_B}=-32i+15j+13k \space\space\space N-m$