document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259977>Question 259977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let y=(-7,-6,-2), u1=(6,-6,1), u2=(-4,2,36).  Compute the distance d from y to the plane in R3, spanned by u1 and u2.  The distance d is supposed to be the shortest distance and I understand that to be the length from y to where it is perpendicular to the plane.  The confusion is with a method that uses a normal vector to the plane and is that now considered the projection of y onto the normal vector such that I am now looking for the parallel component of y on a?  Can you provide a visual model perhaps? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191590 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=191590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the basic outline to solving this problem.\r<BR>\n" );
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document.write( "1) First find the equation of the plane. To do this, compute the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Cross_product\">cross product</a> of u1 and u2 to find a third vector (say u3). This vector is the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Surface_normal\">normal</a> which will help you find the equation of the plane.\r<BR>\n" );
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document.write( "2) This normal will essentially be a line. So you can find the equation of that line using that normal vector and the vector (-7, -6, -2) (since you want the line to go through this point)\r<BR>\n" );
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document.write( "3) Use both the line and the plane to find the intersection between the two figures. This point will be closest to the given point (-7, -6, -2)\r<BR>\n" );
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document.write( "4) Finally, find the distance (using the distance formula) from the point found in step 3 and (-7, -6, -2) to find the distance from (-7, -6, -2) to the plane.\r<BR>\n" );
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document.write( "Let me know if this helps. If not, then repost or ask me. </SPAN>\n" );
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