Question

A force of magnitude $6$ in the direction of the vector $\overrightarrow{i}-2\overrightarrow{j}+2\overrightarrow{k}$ acts at the point whose position vector is $\overrightarrow{i}-\overrightarrow{j}$. A second force acting at the point with position vector $\overrightarrow{j}-\overrightarrow{k}$ forms a couple with the first force. Find the vector moment of the couple.

• A. $-(2\overrightarrow{i}+\overrightarrow{j})$
• B. $-2(2\overrightarrow{i}+\overrightarrow{j})$
• C. $-4(2\overrightarrow{i}+\overrightarrow{j})$
• D. $-8(2\overrightarrow{i}+\overrightarrow{j})$

Answer 1

The correct option is B $-2(2\overrightarrow{i}+\overrightarrow{j})$

Force is: $F=\frac{6}{3}(\hat{i}-2\hat{j}+2\hat{k})$

And the distance between the two positions are: $r={\overrightarrow{r}}_1-{\overrightarrow{r}}_2=(\hat{i}-2\hat{j}+\hat{k})$

So the moment vector is: $\overrightarrow{M}=\overrightarrow{r}\times \overrightarrow{F}=-2(2\hat{i}+\hat{j})$