Additive inverse for elliptic curve addition in finite field in jacobian coordinates
The projective form of Weierstrass equation of an elliptic curve is obtained by replacing $x$ by $X/Z^c$ and $y$ by $Y/Z^d$. If $c=d=1$ then we have standard projective coordinates. In this state, point at infinity is $(0:1:0)$. But in Jacobian coordinates($c=2$ and $d=3$), point at infinity is $(1:1:0)$.

As poncho said in comments, The additive inverse of the point $(X:Y:Z)$ is  $(X:-Y:Z)$ .