A: Hello,Lily. ____?

B: I' m going to have a party for my 14th birthday this weekend.

A: Oh, that's wonderful! ____?

B: I will have it at home. ____? I'll be happy if you can come.

A: Sure, I'd love to. And I'll bring some cakes made by my mom. She's good at baking (烘焙), you know.

B: Thanks.

A: ____ ?

B: It will start at 10 o'clock on Saturday morning. After that, how about going to the park?

A: ____! We can fly a kite there.

B: OK. See you then.

如图，直三棱柱ABC﹣A₁B₁C₁，底面△ABC中，CA=CB=1，∠BCA=90°，棱AA₁=2，M、N分别是A₁B₁、A₁A的中点．

（1）求$\overrightarrow{BN}$的长；

（2）求cos（$\overrightarrow{B{A}_1}$•$\overrightarrow{C{B}_1}$）的值；

（3）求证A₁B⊥C₁M．