如图，三棱柱\(ABC-A_{1}B_{1}C_{1}\)中，侧棱\(AA_{1}\)垂直底面\(A_{1}B_{1}C_{1}\)，底面三角形\(A_{1}B_{1}C_{1}\)是正三角形，\(E\)是\(BC\)中点，则下列叙述正确的是\((\) \()\)
A. \(CC_{1}\)与\(B_{1}E\)是异面直线
B. \(AE\)与\(B_{1}\)\(C\)\({\,\!}_{1}\)是异面直线，且\(AE⊥B\)\({\,\!}_{1}\)\(C\)\({\,\!}_{1}\) C. \(AC⊥\)平面\(ABB_{1}\)\(A\)\({\,\!}_{1}\) D. \(A_{1}\)\(C\)\({\,\!}_{1}\)\(/\!/\)平面\(AB\)\({\,\!}_{1}\)\(E\)
