高二數(shù)學(xué)點(diǎn)到平的面距離

3．8點(diǎn)到平面的距離Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.

3.8課堂互動(dòng)講練知能優(yōu)化訓(xùn)練課前自主學(xué)案學(xué)習(xí)目標(biāo)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.學(xué)習(xí)目標(biāo)1.掌握點(diǎn)到平面的距離的概念，并會(huì)求點(diǎn)到平面的距離．2．能利用直線的方向向量和平面的法向量求空間中的各種距離．3．體會(huì)向量方法在研究立體幾何中的作用．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.課前自主學(xué)案溫故夯基Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.知新益能垂線長(zhǎng)度dEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.|AP1|Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.思考感悟在求兩條異面直線的距離，直線到平面的距離，兩個(gè)平面間的距離時(shí)能轉(zhuǎn)化為點(diǎn)到平面的距離求解嗎？提示：能．因?yàn)橹本€與平面平行，兩個(gè)平面平行時(shí)，直線上的點(diǎn)或其中一個(gè)平面上的點(diǎn)到另一個(gè)平面的距離均相等，而兩條異面直線可以構(gòu)造線面平行，所以在求以上距離時(shí)均可轉(zhuǎn)化為點(diǎn)到平面的距離．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.課堂互動(dòng)講練點(diǎn)到直線的距離考點(diǎn)突破Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.在長(zhǎng)方體ABCD-A1B1C1D1中，AA1＝AB＝2，AD＝1，點(diǎn)F，G分別是AB，CC1的中點(diǎn)，求點(diǎn)D1到直線GF的距離．例1【思路點(diǎn)撥】建系后按求點(diǎn)線距離的步驟求解．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.【名師點(diǎn)評(píng)】

(1)在直線上選取點(diǎn)時(shí)，可視情況靈活選擇，原則是便于計(jì)算．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.點(diǎn)到平面的距離點(diǎn)到平面的距離的求法：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.例2Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.【思路點(diǎn)撥】建立空間直角坐標(biāo)系，利用坐標(biāo)運(yùn)算求解．【解】作AP⊥CD于點(diǎn)P.如圖，分別Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.【名師點(diǎn)評(píng)】利用向量法求點(diǎn)到平面的距離，關(guān)鍵是找到平面的法向量．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.若直線a∥平面α，則直線a上的任意一點(diǎn)到平面的距離都相等；若平面α∥平面β，則平面α上任意一點(diǎn)到平面β的距離也都相等．因此直線到平面的距離以及兩平行平面間的距離都可轉(zhuǎn)化為點(diǎn)到平面的距離解決．求線面距和面面距Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.例3【思路點(diǎn)撥】因?yàn)橹本€A1B1∥平面ABE，所以A1B1到平面ABE的距離等于點(diǎn)A1到平面ABE的距離，從而轉(zhuǎn)化為點(diǎn)到平面的距離求解．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.【解】如圖，以D為原點(diǎn)，分別以DA、DC、DD1所在直線為x軸、y軸、z軸建立空間直角坐標(biāo)系，Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.【名師點(diǎn)評(píng)】求直線與平面間的距離，往往轉(zhuǎn)化為點(diǎn)到平面的距離求解，且這個(gè)點(diǎn)要適當(dāng)選取，以求解最為簡(jiǎn)單為準(zhǔn)則，但在求點(diǎn)到平面的距離時(shí)，有時(shí)用直線到平面的距離進(jìn)行過(guò)渡．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.自我挑戰(zhàn)在棱長(zhǎng)為1的正方體ABCD

A1B1C1D1中，M、N、E、F分別是A1B1、A1D1、B1C1、C1D1的中點(diǎn)，求平面AMN與平面EFDB的距離．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientP