$A$ force of $(5\hat i + 6\hat j - 7\hat k) \, N$ is applied to a body of mass $10 \, kg$,causing it to displace from position $(4\hat i - 2\hat j + 5\hat k) \, m$ to $(8\hat i + 6\hat j - 3\hat k) \, m$. Calculate the work done in $J$.

$A$ force $\vec F = 2\hat i - 3\hat j + 7\hat k \text{ (N)}$ acts on a particle which undergoes a displacement of $\vec S = 7\hat i + 3\hat j - 2\hat k \text{ (m)}$. Calculate the work done by the force in $J$.

If force and displacement of a particle in the direction of force are doubled,the work done would be:

$A$ particle of mass $m$ is projected with speed $u$ at angle $\theta$ with the horizontal from the ground. The work done by gravity on it during its upward motion is ..........

What is required for work to be done when a force is applied to an object?

Two persons $A$ and $B$ perform the same amount of work in moving a body through a certain distance $d$ with the application of forces acting at angles $45^{\circ}$ and $60^{\circ}$ with the direction of displacement,respectively. The ratio of the force applied by person $A$ to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is ...... .