$A$ force $\vec F = (5\hat i + 3\hat j) \ N$ is applied to a particle,which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j) \ m$. The work done on the particle is ......... $J$.

$A$ 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 $J$?

$A$ person draws water from a $5\,m$ deep well using a bucket of mass $2\,kg$ and capacity $8\,litre$ with a rope of mass $1\,kg.$ What is the total work done by the person? (Assume $g = 10\,m/s^2$ and the density of water is $1\,kg/litre$.)

$A$ particle moves from a point $(-2\hat i + 5\hat j) \ m$ to $(4\hat j + 3\hat k) \ m$ when a force of $(4\hat i + 3\hat j) \ N$ is applied. How much work has been done by the force? $J$

$A$ 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 $............ \text{ J}$.

$A$ particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec{F} = (3\hat{i} + 4\hat{j})$ through two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then