Chapter 6.12, Problem 16MP

Given $F_1=2xzi+yj+x^{2}k$ and $F_2=yi-xj:$

(a) Which $F$, if either, is conservative?

(b) If one of the given $F^{\prime }$ s is conservative, find a function $W$ so that $F=\nabla W$.

(c) If one of the $F^{\prime }$ s is neoconservative, use it to evaluate ${\displaystyle \int F}\cdot dr$ along the straight line from $(0,1)$ to $(1,0)$.

(d) Do part (c) by applying Green’s theorem to the triangle with vertices (0,0), $(0,1),(1,0)$.