$A$ force $\vec F = 3\hat i + c\hat j + 2\hat k$ acting on a particle causes a displacement $\vec S = - 4\hat i + 2\hat j - 3\hat k$. If the work done is $6 \ J$,then the value of $c$ will be:

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

$A$ rope is used to lower a block of mass $M$ vertically downwards by a distance $x$ with a constant downward acceleration of $g/2$. What is the work done by the rope on the block?

$A$ force $\vec{F}=(3 \hat{i}+4 \hat{j}) \;N$ acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle first moves along the $x$-axis to the point $(4,0) \;m$ and then parallel to the $y$-axis to the point $(4,3) \;m$. The total work done by the force on the particle is ............. $J$.

$A$ 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 $c$.

$A$ force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$. What will be the value of $b$,if the work done on the particle is zero?