$A$ force $\vec F = 6\hat i + 2\hat j - 3\hat k$ acts on a particle,causing a displacement $\vec d = 2\hat i - 3\hat j + c\hat k$. If the work done during this process is zero,find the value of $c$.

$A$ body constrained to move along the $z$-axis of a coordinate system is subject to a constant force $F$ given by $F = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$,where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the $x, y,$ and $z$-axes of the system respectively. What is the work done (in $J$) by this force in moving the body a distance of $4 \text{ m}$ along the $z$-axis?

If $\vec{F}$ and $\vec{S}$ are force and displacement respectively,and the work done by them is zero,then:

$A$ particle moves from position $3\hat i + 2\hat j - 6\hat k$ to $14\hat i + 13\hat j + 9\hat k$ due to a uniform force of $(4\hat i + \hat j + 3\hat k) \, N$. If the displacement is in meters,the work done will be ......... $J$.

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

$A$ cubical vessel of height $1 \,m$ is full of water. What is the amount of work done in pumping water out of the vessel (in $\,J$)? (Take $g = 10 \,m \,s^{-2}$)