document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=882303>Question 882303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> points A(3,-5,1) and B(2,1,2) and C (1,-3,3) lie on a plane. Find the exact distance from X (2,-1,3) to the plane   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #533065 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=533065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the equation of the plane.<BR>\n" );
document.write( "AB=(-1,6,1)<BR>\n" );
document.write( "BC=(-1,-4,1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=ABxBC=%28matrix%283%2C3%2Ci%2Cj%2Ck%2C-1%2C6%2C1%2C-1%2C-4%2C1%29%29 ALIGN=MIDDLE  ALT=\"n=ABxBC=%28matrix%283%2C3%2Ci%2Cj%2Ck%2C-1%2C6%2C1%2C-1%2C-4%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=i%286%281%29-%28-4%29%281%29%29%2B%28%281%29%28-1%29-%281%29%28-1%29%29j%2B%28%28-1%29%28-4%29-%28-1%29%286%29%29k ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10i%2B0j%2B10k ALIGN=MIDDLE  ALT=\"n=10i%2B0j%2B10k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28matrix%281%2C3%2Cx-3%2Cy%2B5%2Cz-1%29%29=0 ALIGN=MIDDLE  ALT=\"n%2A%28matrix%281%2C3%2Cx-3%2Cy%2B5%2Cz-1%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28x-3%29%2B0%28y%2B5%29%2B10%28z-1%29=0 ALIGN=MIDDLE  ALT=\"10%28x-3%29%2B0%28y%2B5%29%2B10%28z-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-30%2B10z-10=0 ALIGN=MIDDLE  ALT=\"10x-30%2B10z-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B10z=40 ALIGN=MIDDLE  ALT=\"10x%2B10z=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%2Bz=4%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%2Bz=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "Now that you have the equation of the plane,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=abs%28ax%5B0%5D%2Bby%5B0%5D%2Bcz%5B0%5D%2Bd%29%2Fsqrt%28a%5E2%2Bb%5E2%2Bc%5E2%29 ALIGN=MIDDLE  ALT=\"L=abs%28ax%5B0%5D%2Bby%5B0%5D%2Bcz%5B0%5D%2Bd%29%2Fsqrt%28a%5E2%2Bb%5E2%2Bc%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where the plane is defined by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2Bby%2Bcz%2Bd=0 ALIGN=MIDDLE  ALT=\"ax%2Bby%2Bcz%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the point is <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B0%5D ALIGN=MIDDLE  ALT=\"z%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-4 ALIGN=MIDDLE  ALT=\"d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=abs%281%282%29%2B1%283%29-4%29%2Fsqrt%281%5E2%2B0%5E2%2B1%5E2%29 ALIGN=MIDDLE  ALT=\"L=abs%281%282%29%2B1%283%29-4%29%2Fsqrt%281%5E2%2B0%5E2%2B1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=abs%282%2B3-4%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"L=abs%282%2B3-4%29%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"L=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=sqrt%282%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28L=sqrt%282%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );