(3) (1) If the solution set of the inequality $|x-1|-|x-2|<a$ with respect to $x$ is $\mathbf{R}$, find the range of real number $a$;
(2) If the inequality $|x-1|-|x-2|<a$ with respect to $x$ has real solutions, find the range of real number $a$;
(3) If the solution set of the inequality $|x-1|-|x-2|<a$ with respect to $x$ is $\varnothing$, find the range of real number $a$.
(3) (1) $a>1$
(2) $a>-1$
(3) $a \leqslant-1$