document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=50437>Question 50437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a vector normal to the surface z + 2xy = x^2 + y^2 at the point (1,1,0). <BR>\n" );
document.write( "Normally I would use gradient g(x,y,z)=0 or f(x,y)= x^2 -2xy + y^2 -z but I can't make it work??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #33519 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=33519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find a vector normal to the surface z + 2xy = x^2 + y^2 at the point...P SAY.. (1,1,0).<BR>\n" );
document.write( "Normally I would use gradient g(x,y,z)=0 or f(x,y)= x^2 -2xy + y^2 -z but I can't make it work???<BR>\n" );
document.write( "LET US USE SAME METHOD SUGGESTED BY YOU..<BR>\n" );
document.write( "F=X^2+Y^2-2XY-Z=0...<BR>\n" );
document.write( "GRAD(F)=i(DF/DX)+j(DF/DY)+k(DF/DZ)....WHERE THE DERIVATIVES ARE ALL PARTIAL DERIVATIVES.HOPE YOU KNOW IT...THIS MEANS WE KEEP ALL VARIABLES EXCEPT ONE UNDER CONSIDERATION CONSTANT .WE FIND THEM ALL AT THE GIVEN POINT P SAY X=1,Y=1,Z=0<BR>\n" );
document.write( "DF/DX=2X-2Y..=2-2=0<BR>\n" );
document.write( "DF/DY=2Y-2X...=0<BR>\n" );
document.write( "DF/DZ=-1...=-1<BR>\n" );
document.write( "HENCE NORMAL TO THE PLANE IS <BR>\n" );
document.write( "N=GRAD(F)= -k </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );