document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30815>Question 30815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: The point A(x0, y0, z0) lies outside a plane Q with equation ax+by+cz+d=0. The point P(x, y, z) lies on the plane Q. AB is the distance between the point A and the plane Q (B is a point ON plane Q). \r<BR>\n" );
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document.write( "Derive the equation: (AB)= | ax0+by0+cz0+d | / sq.root of (a^2+b^2+c^2).\r<BR>\n" );
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document.write( "Basically, this question is asking you to derive the generality of finding the distance from a point to a plane. Any help is GREATLY appreciated, I would like it by tomorrow if possible!!\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "-Stephanie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17642 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=17642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: The point A(x0, y0, z0) lies outside a plane Q with equation ax+by+cz+d=0.<BR>\n" );
document.write( "DIRECTION RATIOS OF NORMAL TO PLANE ARE A,B AND C.\r<BR>\n" );
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document.write( " The point P(x, y, z) lies on the plane Q. AB is the distance between the point A and the plane Q (B is a point ON plane Q).<BR>\n" );
document.write( "SO AB IS PERPENDICULAR TO PLANE OR PARALLEL TO ITS NORMAL.<BR>\n" );
document.write( "LET COORDINATES OF B BE P,Q,R.<BR>\n" );
document.write( "SO DIRECTION RATIOS OF AB ARE <BR>\n" );
document.write( "P-X0,Q-Y0,R-Z0.<BR>\n" );
document.write( "THESE ARE IN SAME RATIO AS THAT OF NORMAL AS BOTH ARE PARALLEL.HENCE<BR>\n" );
document.write( "(P-X0)/A = (Q-Y0)/B = (R-Z0)/C =K SAY<BR>\n" );
document.write( "SO...<BR>\n" );
document.write( "P=X0+AK<BR>\n" );
document.write( "Q=Y0+BK<BR>\n" );
document.write( "R=Z0+CK<BR>\n" );
document.write( "BUT B(P,Q,R)IS ON PLANE.<BR>\n" );
document.write( "HENCE <BR>\n" );
document.write( "AP+BQ+CR+D=0<BR>\n" );
document.write( "A(X0+AK)+B(Y0+BK)+C(Z0+CK)+D=0<BR>\n" );
document.write( "K(A^2+B^2+C^2)=-AX0-BY0-CZ0-D<BR>\n" );
document.write( "K*SQRT{A^2+B^2+C^2)=-(AX0+BY0+CZ0+D)/SQRT.{(A^2+B^2+C^2)}\r<BR>\n" );
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document.write( "AB=DISTANCE OF POINT FROM PLANE =SQRT.{(P-X0)^2+(Q-Y0)^2+(R-Z0)^2}<BR>\n" );
document.write( "=SQRT.{(AK)^2+(BK)^2+(CK)^2}=K*SQRT{A^2+B^2+C^2}<BR>\n" );
document.write( "=-(AX0+BY0+CZ0+D)/SQRT.{(A^2+B^2+C^2)}<BR>\n" );
document.write( "IT IS USUALLY PUT AS MODULUS OF THE ABOVE RATIO...\r<BR>\n" );
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document.write( "Derive the equation: (AB)= | ax0+by0+cz0+d | / sq.root of (a^2+b^2+c^2).<BR>\n" );
document.write( "Basically, this question is asking you to derive the generality of finding the distance from a point to a plane. Any help is GREATLY appreciated, I would like it by tomorrow if possible!!<BR>\n" );
document.write( "Thanks, </SPAN>\n" );
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