Question

A constant force $\overrightarrow{F}=3\hat{i}+2\hat{j}+4\hat{k}$ is applied at the point $(1,0,1)$, then the vector moment of $\overrightarrow{F}$ about the point $(1,2,3)$ is

• A. $4\hat{i}+6\hat{j}-6\hat{k}$
• B. $4\hat{i}-6\hat{j}-6\hat{k}$
• C. $6\hat{i}-4\hat{j}+6\hat{k}$
• D. $-6\hat{i}-4\hat{j}+6\hat{k}$

Answer 1

The correct option is A $4\hat{i}+6\hat{j}-6\hat{k}$

The vector moment of a force about a point is given by $\overrightarrow{r}\times \overrightarrow{F}$ where $\overrightarrow{r}$ is the vector from the point of application of force to the point about which moment is being taken.

$\overrightarrow{r}=2\hat{j}+2\hat{k}$

Moment $=(2\hat{j}+2\hat{k})\times (3\hat{i}+2\hat{j}+4\hat{k})$
$=-6\hat{k}+8\hat{i}+6\hat{j}-4\hat{i}$
$=4\hat{i}+6\hat{j}-6\hat{k}$