A) \[\vec{i}+2\vec{j}-4\vec{k}\]
B) \[\vec{i}-2\vec{j}-4\vec{k}\]
C) \[\vec{i}+2\vec{j}+4\vec{k}\]
D) \[\vec{i}-2\vec{j}+4\vec{k}\]
Correct Answer: C
Solution :
Force \[(\vec{F})=2\vec{i}+\vec{j}-\vec{k}\]and its position vector \[=2\vec{i}-\vec{j}.\] We know that the position vector of a force about origin \[(\vec{r})=(2\vec{i}-\vec{j})-(0\vec{i}+0\vec{j}+0\vec{k})\] or \[\vec{r}=2\vec{i}-\vec{j}\] Therefore, moment of the force about origin \[=\vec{r}\times \vec{F}=\left| \begin{matrix} i & j & k \\ 2 & -1 & 0 \\ i & 1 & -1 \\ \end{matrix} \right|=\vec{i}+2\vec{j}+4\vec{k}\]
You need to login to perform this action.
You will be redirected in
3 sec
