document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62453>Question 62453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P1 be the plane defined by the points:\r<BR>\n" );
document.write( "\n" );
document.write( "(-1,-2,-3), (-3,1,-5) and (2,-5,-4)\r<BR>\n" );
document.write( "\n" );
document.write( "Find the equation of the plane perpendicular to P1 and containing the line:\r<BR>\n" );
document.write( "\n" );
document.write( "(x,y,z) = (2,-2,-3) + t (2,-3,0)\r<BR>\n" );
document.write( "\n" );
document.write( "Your answer should be in the form Ax + By + Cz - D = 0. <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 #43465 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=43465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let P1 be the plane defined by the points:<BR>\n" );
document.write( "Q=(-1,-2,-3), R=(-3,1,-5) and S=(2,-5,-4)<BR>\n" );
document.write( "Find the equation of the plane perpendicular to P1 and containing the line:<BR>\n" );
document.write( "L1 SAY =(x,y,z) = (2,-2,-3) + t (2,-3,0)<BR>\n" );
document.write( "EQN. OF REQUIRED PLANE IS <BR>\n" );
document.write( "A(X-2)+B(Y+2)+C(Z+3)=0..............1..WITH DRS OF A,B,C.<BR>\n" );
document.write( "DRS OF L1 ARE 2,-3,0...IT IS PERPENDICULAR TO NORMAL O REQD.PLANE.HENCE<BR>\n" );
document.write( "2A-3B=0.......A=1.5B.........2<BR>\n" );
document.write( "DRS OF NORMAL TO PLANE P1 IS GIVEN BY CROSS PRODUCT OF JOINS OF QR AND RS<BR>\n" );
document.write( "DRS OF QR = [-3+1,1+2,-5+3]= [-2,3,-2] <BR>\n" );
document.write( "DRS OF RS = [2+3,-5-1,-4+5]= [5,-6,1]<BR>\n" );
document.write( "QR X RS = [-2i+3j-2k]X[5i-6j+k]= 12k+2j-15k+3i-10j-12i=-9i-8j-3k<BR>\n" );
document.write( "THIS SHOULD BE PERPENDICULAR TO NORMAL OF REQD.PLAN.HENCE<BR>\n" );
document.write( "-9A-8B-3C=0......9A+8B+3C=0...........3<BR>\n" );
document.write( "9*1.5B+8B+3C=0<BR>\n" );
document.write( "21.5B=-3C<BR>\n" );
document.write( "C=-21.5B/3<BR>\n" );
document.write( "TAKING B AS 6 , WE GET A = 9...C=-43<BR>\n" );
document.write( "HENCE EQN.OF REQD PLANE IS <BR>\n" );
document.write( "9(X-2)+6(Y+2)-43(Z+3)=0<BR>\n" );
document.write( "9X+6Y-43Z-135=0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer should be in the form Ax + By + Cz - D = 0.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );