oldlee 发表于 2006-5-16 20:26:00

[灌水]关于点到面的距离

<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none">如图所示：在梯形ABCD中，AD//BC，<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shapetype id=_x0000_t75 coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> 角ABC=</v:shapetype>90&shy;o，AB=1，AD=3，角ADC=27o，PA与平面ABCD垂直，PA=1，求点A到平面PDC的距离：<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></P>

ahlzl 发表于 2006-5-16 22:25:00

0.80606028

oldlee 发表于 2006-5-17 20:15:00

<P>谢谢版主的光顾!</P>
<P>&nbsp;</P>

zgzzsn 发表于 2006-6-1 18:35:00

<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt 18pt; TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt"><B style="mso-bidi-font-weight: normal"><SPAN style="mso-list: Ignore"><FONT face="Times New Roman">1.<SPAN style="FONT: 7pt 'Times New Roman'">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </FONT></SPAN></SPAN></B><B style="mso-bidi-font-weight: normal">把坐标系移到平面ＰＤＣ：<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><B style="mso-bidi-font-weight: normal"><o:p><FONT face="Times New Roman">&nbsp;</FONT></o:p></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">命令<FONT face="Times New Roman">: _ucs</FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">当前<FONT face="Times New Roman"> UCS </FONT>名称<FONT face="Times New Roman">: *</FONT>没有名称<FONT face="Times New Roman">*</FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">输入选项<FONT face="Times New Roman"> </FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5"><FONT face="Times New Roman">[</FONT>新建<FONT face="Times New Roman">(N)/</FONT>移动<FONT face="Times New Roman">(M)/</FONT>正交<FONT face="Times New Roman">(G)/</FONT>上一个<FONT face="Times New Roman">(P)/</FONT>恢复<FONT face="Times New Roman">(R)/</FONT>保存<FONT face="Times New Roman">(S)/</FONT>删除<FONT face="Times New Roman">(D)/</FONT>应用<FONT face="Times New Roman">(A)/?/</FONT>世界<FONT face="Times New Roman">(W)] </FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5"><FONT face="Times New Roman">&lt;</FONT>世界<FONT face="Times New Roman">&gt;: _3</FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">指定新原点<FONT face="Times New Roman"> &lt;0,0,0&gt;:</FONT>选ｃ</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">在正<FONT face="Times New Roman"> X </FONT>轴范围上指定点<FONT face="Times New Roman"> &lt;220269.9265,0.0000,0.0000&gt;:</FONT>选Ｄ</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">在<FONT face="Times New Roman"> UCS XY </FONT>平面的正<FONT face="Times New Roman"> Y </FONT>轴范围上指定点<FONT face="Times New Roman"> &lt;220268.9265,-1.0000,0.0000&gt;:</FONT>选ｐ</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><o:p><FONT face="Times New Roman">&nbsp;</FONT></o:p></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><B style="mso-bidi-font-weight: normal"><FONT face="Times New Roman">2.</FONT></B><B style="mso-bidi-font-weight: normal">把光标放在Ａ点，在下面状态行显示的Ｚ坐标值就是Ａ点到平面<FONT face="Times New Roman">PDC</FONT></B><B style="mso-bidi-font-weight: normal">的距离.<o:p></o:p></B></P>

zgzzsn 发表于 2006-6-1 21:58:00

关于点到面的距离

zgzzsn 发表于 2006-6-1 22:04:00

<P>还可以用矢量解，用ｅｘｃｅｌ。</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">已知：平面π的方程<SPAN style="mso-text-raise: -5.0pt"><?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shape id=_x0000_i1025 style="WIDTH: 105.75pt; HEIGHT: 15.75pt" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///D:/Temp/msoclip1/01/clip_image001.wmz"></v:imagedata></v:shape></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">　　　平面外一点Ｍ</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">点Ｍ到平面π的距离</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">在这里：</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">平面π的方程：由三点确定：</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<o:p></o:p></FONT></P>
<DIV align=center>
<TABLE style="WIDTH: 198pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0cm 0cm 0cm 0cm" cellSpacing=0 cellPadding=0 width=264 border=0>
<TBODY>
<TR style="HEIGHT: 14.25pt">
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 35pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=47>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 54pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=72>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">xi<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 51pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">yi<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 58pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=77>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">zi<o:p></o:p></FONT></P></TD></TR>
<TR style="HEIGHT: 14.25pt">
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right>ｐ<o:p></o:p></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">0<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">0<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">1<o:p></o:p></FONT></P></TD></TR>
<TR style="HEIGHT: 14.25pt">
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right>ｃ<o:p></o:p></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">1.037389<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">-1<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">0<o:p></o:p></FONT></P></TD></TR>
<TR style="HEIGHT: 14.25pt">
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right>ｄ<o:p></o:p></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">3<o:p></o:p></FONT></P></TD>
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<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">0<o:p></o:p></FONT></P></TD>
<TD style="BORDER-RIGHT: #d4d0c8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 0.75pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt" vAlign=bottom noWrap>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right><FONT face="Times New Roman">0<o:p></o:p></FONT></P></TD></TR></TBODY></TABLE></DIV>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<o:p></o:p></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 63pt"></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 63pt"><FONT face="Times New Roman"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">点Ｍ到平面π的距离＝0.806060281</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<o:p></o:p></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">具体解法用<FONT face="Times New Roman">excel</FONT>更方便。见ＥＸＣＥＬ附件</P>

zgzzsn 发表于 2006-6-1 22:07:00

还有一个附件

还有一个附件
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