如图，三棱柱\(ABC-A_{1}B_{1}C_{1}\)中，侧面\(AA_{1}C_{1}C⊥\)侧面\(ABB_{1}A_{1}\)，\(AC=AA_{1}= \sqrt {2}AB\)，\(∠AA_{1}C_{1}=60^{\circ}.AB⊥AA_{1}\)，\(H\)为棱\(CC_{1}\)的中点，\(D\)为\(BB_{1}\)的中点．
\((\)Ⅰ\()\)求证：\(A_{1}D⊥\)平面\(AB_{1}H\)；
\((\)Ⅱ\()AB= \sqrt {2}\)，求三棱柱\(ABC-A_{1}B_{1}C_{1}\)的体积．