如图已知正方体\(ABCD-{A}_{1}{B}_{1}{C}_{1}{D}_{1}\)，\(M\)，\(N\)分别是\({A}_{1}D\)，\({D}_{1}B\)的中点，则\((\quad)\)
A. 直线\(A_{1}D\)与直线\(D_{1}B\)垂直，直线\(MN//\)平面\(ABCD\)
B. 直线\(A_{1}D\)与直线\(D_{1}B\)平行，直线\(MN⊥\)平面\(BDD_{1}B_{1}\) C. 直线\(A_{1}D\)与直线\(D_{1}B\)相交，直线\(MN//\)平面\(ABCD\) D. 直线\(A_{1}D\)与直线\(D_{1}B\)异面，直线\(MN⊥\)平面\(BDD_{1}B_{1}\)
