Consider a force given by a two-dimensional field \(\vec F\left( {x,y} \right) = \left( {{x^2} - {y^2}} \right)\hat i + 2xy\hat j\). The three different paths connecting the origin O(0, 0) to the point P(2, 1) are shown below:
Which of the following is/are true?
1
The work done by a force along the path 1 is \(\frac{{10}}{3}\)
2
The work done by a force along the path 2 is \(\frac{{10}}{3}\)
3
The work done by a force along the path 3 is \(\frac{{2}}{3}\)
4
The integral is independent of the path.