World War II lasted from 1939 to 1945. Life changed for everybody, including women and children because of the war. Millions of people lost their lives during the war. The Diary of a Young Girl was a record of that time. The book was written by a girl named Anne Frank.

    Anne Frank was born in Germany in June 1929. Because the German Nazi(纳粹分子) hated the Jews(犹太人) and warned to kill them, her family had to move to another country. In July 1942, they went into hiding in a secret place in her father's office. During that difficult time, Anne kept writing diaries until she and her family were discovered by the Nazis in August 1944. They were caught and sent to a Nazi camp. The next year, her mother died. In the same year, she and her elder sister died of illness, before the war ended.

    After the war, her father collected her diaries and the book The Diary of a Young Girl came out in 1947. It has been put into over 30 languages since then. The book has been read by people all over the world. In her diary, Anne wrote down her thoughts, her feelings, her hopes and her dreams for the future, "I want the diary to be my friend, and I'm going to call this friend Kitty." "I can't spend all day complaining because it's impossible to have any fun! ... Every day, I feel the beauty of nature and the goodness of the people around me. With all that, why should 1 be sad?"

    The Diary of a Young Girl has also become a symbol of the greatness of the human spirit. It is called one of the wisest and most moving records on war.

（Ⅰ）求证：C₁B⊥平面ABC；

（Ⅱ）E是棱CC₁所在直线上的一点，若二面角A﹣B₁E﹣B的正弦值为 $\frac{1}{2}$ ，求CE的长．

阅读下文，回答相关问题。

                                                                                                                                           阳光下的守望
        ①我见过一个母亲，一个阳光下守望的母亲。母亲就站在七月炙热的阳光下翘首望着百米外的考场，神色凝重。母亲脸上早已狼藉着豆大的汗珠，汗水早就将她的衣衫浸得水洗一样，她的花白的头发凌乱地贴在前额上。母亲就这样半张着嘴，一动不动地盯着考场，站成了一尊雕像。
        ②树阴下说笑的家长停止了说笑，他们惊讶地望着阳光下的母亲。有人劝母亲挪到树阴下，母亲神情肃然的脸上挤出个比仲春的冰还薄的笑，小声嗫嚅道：“站在这里能清清楚楚地看到考场，能清清楚楚地看到孩子。”
        ③没人笑她痴，没人笑她傻，也没人再劝她。
        ④烈日下守望的母亲舔了舔干裂的嘴唇，目光扫了扫不远处的茶摊，就目不转睛地盯着考场。不知过了多久，也许是半个小时，也许是一个小时，母亲就像摊软泥一样瘫在了地上。众人一声惊呼后都围了上去，看千呼万唤后她仍是昏迷不醒，便将她抬到学校大门口的医务室里。
        ⑤听了心跳，量了血压，挂了吊针，母亲仍然紧闭着双眼。经验丰富的医生微笑着告诉众人：“看我怎样弄醒她。”
        ⑥医生附在母亲耳边，轻轻地说了句：“学生下考场了。”母亲猛地从床上坐起来，拔掉针头，下了病床：“我得赶快问问儿子考得怎么样。”
        ⑦我常常将这个真实的故事讲给我的学生听，学生说，这个故事抵得上一千句枯燥无味的说教。

                                                                                                                                                                                                                          （《阳光下的守望》）