設m,n是兩條不同直線,α、β是兩個不同平面,有下列命題:                          ...

問題詳情:

設m,n是兩條不同直線,α、β是兩個不同平面,有下列命題:                          ...

設m,n是兩條不同直線,α、β是兩個不同平面,有下列命題:                                  

①若α⊥β,m⊥α,則m不可能與β相交                                                              

②若m⊥n,m⊥α,則n不可能與α相交                                                               

③若m∥α,n∥α,則m與n一定平行                                                                  

④若m⊥β,n⊥α,則α與β一定垂直                                                                   

其中真命題的序號爲(  )                                                                                

A.①②                            B.②③                             C.①④                             D.②④

【回答】

A【分析】利用直線與平面平行與垂直,面面垂直的*質和判斷,分析4個選項,即可得出結論.                  

【解答】解:①若α⊥β,m⊥α,則m∥β或m⊂β,故①正確;                                  

②若m⊥n,m⊥α,則n∥α或n⊂α,故②正確;                                                 

③若m∥α,n∥α,則m與n平行、相交或異面,故③不正確;                                   

④若m⊥β,n⊥α,則α與β可以平行,故④不正確.                                                 

故選:A.                                                                                                          

【點評】本題考查直線與平面平行與垂直,面面垂直的*質和判斷的應用,考查邏輯推理能力,屬於中檔題.                                                      

                                                                                                                       

知識點:點 直線 平面之間的位置

題型:選擇題