短文改错。假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。文中共有10处语言错误，每句中最多有两处。每处错误涉及一个单词的增加、删除和修改。

增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词。

删除：把多余的词用斜线划掉。

修改：在错的词下划一横线，并在该词下面写出修改后的词。

注意：1.每处错误及其修改均仅限一词；2.只允许修改10处，多者（从第11处起）不计分。

    The winter holiday is coming. My classmates and I are talking about how to do during the holiday. We can chose between staying at home and take a trip. If we stay at home, it is comfortable but there is no need to spend money. But in that case, we will learn little about world. If we go on a trip abroad, we can broaden your view and gain knowledges we cannot get from books. Some classmates suggest we can go to places of interest nearby. I thought that it is a good idea. It does not cost many, yet we can still learn a lot.

已知向量$\overrightarrow{a}=\left(\sin \left(\alpha +\frac{\mathrm{\pi }}{6}\right),1\right),\overrightarrow{b}=\left(4,4\cos \alpha -\sqrt{3}\right)$，若$\overrightarrow{a}\perp \overrightarrow{b}$，则$\sin \left(\alpha +\frac{4\mathrm{\pi }}{3}\right)$等于(      )

—That's why he is suffering from hunger.

    ①一个勇敢自救的人，不仅遇到怎样的险阻，都不会放弃对成功的追求。

    ②当你在艰难的境地里勇往直前的时候，哪怕你只有一根可以活动手指，只要一气呵成地用它去敲击成功之门，总有一天，会敲开那扇门。

    ③在这个世界上，除非你自己放弃，否则没有雷电可以击垮你，没有可以吞没你的巨浪，没有荆棘可以阻挡你。