$A$ 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:

Define work exerted by force.

$A$ small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} \text{ N}$. The value of work done will be $............ \text{ J}$.

$A$ man carries a bucket of weight $60 \ N$ and walks $7 \ m$ in the horizontal direction,then climbs $5 \ m$ in the vertical direction. What is the work done by the man in $J$?

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

$A$ force $\overrightarrow{F} = 5\hat{i} + 6\hat{j} + 4\hat{k}$ acting on a body produces a displacement $\overrightarrow{S} = 6\hat{i} - 5\hat{k}$. The work done by the force is: (in $J$)