问题 填空题

若直线l不平行于平面α,且l⊄α,则①α内的所有直线与l异面;②α内不存在与l平行的直线;③α内存在唯一的直线与l平行;④α内的直线与l都相交.以上结论中正确的是______.(把你认为正确的结论都填上)

答案

因为直线l不平行于平面α,且l不在平面α内,故直线l与平面α相交

设l∩α=O,则

当α内的直线m经过点O时,l、m就是相交直线,不能异面,故①不正确;

由线面平行的判定定理,可得若α内存在与l平行的直线,则直线l就平行于平面α,与题设矛盾,故②不正确;

由②的分析可得,③也不正确;

由①的分析可得,当α内的直线n不经过点O时,l、n就是异面,故④不正确.

故答案为:②

单项选择题 A3/A4型题
单项选择题

A businessman must keep records of the money he takes in and the money he spends. The work of keeping such records is called bookkeeping. The work of deciding how the records should be set up is called accounting. An accountant also finds out, by studying the records, whether or not a business is doing well. The accountant must know many things about the business.

Suppose a man owns a small clothing store, he keeps records that show that he spent money for newspaper advertising and for suits, shirts, shoes, and neckties to sell to his customers. He had to pay a young man to help him in the store. He also paid rent and had other expenses.

At the end of the year, he must take an inventory. That is, he counts how many pieces of clothing he has on hand. Then he must find out exactly how many he sold, how much money he took in, and how much money he spent in running the business. If he took in more than he spent, he made a profit for the year. If he spent more than he took in, he suffered a loss. He depends on his store accounting records to get all this information.The owner of a small clothing store can keep records without much trouble. But a big oil company or a big bank has many difficult accounting problems. The company must know how much money is to be paid by its debtors and how much it owes other companies for supplies. It must know how much it has lost in depreciation, or wear and tear of its equipment. All of this information must be kept in the company’s accounts. Big companies employ many accountants.After a company’s accountants finish their yearly count, their work must be officially examined. Experts from outside company double-check the records to be sure the accounts are correct.

After taking an inventory, if the owner found that he had got more money than he had spent, he made()

A. a profit

B. a loss

C. an income

D. an interest