document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62451>Question 62451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the shortest distance between the two lines:\r<BR>\n" );
document.write( "\n" );
document.write( "(x,y,z) = (2,-1,2) + t(-3,-2,-2)\r<BR>\n" );
document.write( "\n" );
document.write( "(x,y,z) = (-3,4,1) + s(0,2,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thanks  sooo much!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43520 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the shortest distance between the two lines:<BR>\n" );
document.write( "L1 SAY..(x,y,z) = P SAY(2,-1,2) + t(-3,-2,-2)<BR>\n" );
document.write( "L2 SAY (x,y,z) = Q SAY(-3,4,1) + s(0,2,0) <BR>\n" );
document.write( "IT IS PROJECTION OF PQ ON DIRECTION(L,M,N SAY) PERPENDICULAR TO L1 AND L2<BR>\n" );
document.write( "-3L-2M-2N=0........1<BR>\n" );
document.write( "2M=0<BR>\n" );
document.write( "3L=-2N<BR>\n" );
document.write( "N=-1.5L<BR>\n" );
document.write( "LET L=2...M=0....N=-3<BR>\n" );
document.write( "PQ IS (-3-2,4+1,1-2)=(-5,5,-1)<BR>\n" );
document.write( "S.D.= PROJECTION OF PQ ON (2,0,-3) DIRECTION<BR>\n" );
document.write( "[-5*2+1*3)/SQRT(2^2+3^2)=-7/SQRT(13) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );