题目

20.已知三棱柱ABC－A1B1C1中底面边长和侧棱长均为a,侧面A1ACC1⊥底面ABC,A1B＝a.20题图(Ⅰ)求异面直线AC与BC1所成角的余弦值；(Ⅱ)求证A1B⊥面AB1C. 答案：  解:过点B作BO⊥AC,垂足为点O,则BO⊥侧面ACC1A1,连结A1O,  在Rt△A1BO中,A1B＝a,BO＝a,∴A1O＝a,又AA1＝a,AO＝.∴△A1AO为直角三角形,A1O⊥AC,A1O⊥底面ABC.解法一:(Ⅰ)∵ A1C1∥AC,∴ ∠BC1A1为异面直线AC与BC1所成的角.∵ A1O⊥面ABC,AC⊥BO,∴ AC⊥A1B,∴ A1C1⊥A1B.在Rt△A1BC1中,A1B＝a,A1C1＝a,∴ BC1＝a∴cosBC1A1＝,所以,异面直线AC 已知x、y满足约束条件，则z＝2x＋4x的最小值为________