A particle is located at the position vector

r $=(9\mathrm{.}00+10\mathrm{.}00)$ m

and a force exerted on it is given by

F $=(7\mathrm{.}00+6\mathrm{.}00)$ N$.$

$($a$)$

What is the torque acting on the particle about the origin?

$=$

N $$ m

$($b$)$

Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude?

YesNo$$

$($c$)$

Can there be more than one such point?

YesNo$$

$($d$)$

Can such a point lie on the y$-$axis?

YesNo$$

$($e$)$

Can more than one such point lie on the y$-$axis?

YesNo$$

$($f$)$

Determine the position vector of one such point. $($Give a point on the y$-$axis.$)$

r $=$

m