27．如图所示，三棱柱ABC−A1B1C1ABC-A_{1}B_{1}C_{1}ABC−A1B1C1中，AB⊥BCAB\bot BCAB⊥BC，AB=BC=1AB=BC=1AB=BC=1，BB1=2BB_{1}=2BB1=2，B1C=3{B_1}C=\sqrt{3}B1C=3．（1）证明：BC⊥A1CBC\bot A_{1}CBC⊥A1C；（2）若A1C=2A_{1}C=2A1C=2，求三棱柱ABC−A1B1C1ABC-A_{1}B_{1}C_{1}ABC−A1B1C1的体积．
