document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62447>Question 62447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the shortest distance between the plane 2x+4y-2z=6 and the line (x,y,z) = (-1,-2,4) + t(-2,-1,-4).\r<BR>\n" );
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document.write( "Distance =????\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43522 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=43522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the shortest distance between the plane(P SAY) 2x+4y-2z=6 <BR>\n" );
document.write( "and the line(L SAY) (x,y,z) = (Q SAY)(-1,-2,4) + t(-2,-1,-4).<BR>\n" );
document.write( "Distance =???? <BR>\n" );
document.write( "IF L IS NOT PARALLEL TO P THEN S.D=0 AS IT INTERSECTS THE PLANE.<BR>\n" );
document.write( "IF L||P NORMAL TO PLANE IS PERPENDICULAR TO LINE<BR>\n" );
document.write( "DRS OF NORMAL TO PLANE ...(2,4,-2)<BR>\n" );
document.write( "DRS OF LINE ....(-2,-1,-4)<BR>\n" );
document.write( "2*-2+4*-1+-2*-4=-4-4+8=0...HENCE L||P<BR>\n" );
document.write( "SO TAKE ANY POINT ON LINE AND FIND ITS <BR>\n" );
document.write( "PERPENDICULAR DISTANCE FROM THE PLANE.<BR>\n" );
document.write( "ANY POINT ON LINE IS (-1,-2,-4)<BR>\n" );
document.write( "S.D = [2*-1+4*-2+(-2)(-4)-6]/SQRT(2^2+4^2+2^2)<BR>\n" );
document.write( "= -8/SQRT(24)=-2SQRT(6)/3<BR>\n" );
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