Question

A force $F=2i+j-k$ acts at a point A whose position vector is $2i-j.$ Find the moment of F about the origin If the point of application of F moves from the point A to the point B (position vector 2i+j), find the work done by F.

Answer 1

$\overline{r}=2i-j$
$\overline{F}=2i+j-k$

Hence moment of force about origin is

$=\overline{F}\times \overline{r}$
$=(2i+j-k)\times (2i-j)$
$=-i-2j-4k$

And the work done

$=\overline{F}.(r_2-r_1)$
$=(2i+j-k).(2i+j-(2i-j\left)\right)$

$=(2i+j-k).\left(2j\right)$

$=2$ joules