Question

点P为斜三棱柱ABC-A1B1C1的侧棱BB1上一点,PM垂直于BB1交AA1于点M,PN垂直于BB1交CC1于点N

Answer 1

1 ,BB1⊥PM.BB1⊥PN,∴BB1⊥平面PMN.∵CC1‖BB1∴CC1⊥平面PMN.CC1⊥MN.

2 NM²＝PN²+PM²-2PN×PM×cos∠MPN①

注意∠MPN是二面角A-BB1-C的平面角,①式两边同乘BB1²,得到：

[S（ACC1A1）]²＝[S（BCC1B1）]²+[S（ABB1A1]²

-2[S（BCC1B1）]×[S（ABB1A1]cos[二面角A-BB1-C].