document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026390>Question 1026390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of a line passing through (2,-1,3) and is orthogonal to 3x-7y+5z+55=0, where does the line intersect  the plane </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641665 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The normal vector defining the equation of the plane is {3, -7, 5}.<BR>\n" );
document.write( "Let (x,y,z) be a point on the desired line.  Then combined with the given point (2,-1,3) the vector {x-2, y+1, z-3} must be parallel to the vector {3, -7, 5}.<BR>\n" );
document.write( "Hence {x-2, y+1, z-3}  = k{3, -7, 5}\r<BR>\n" );
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document.write( "==> the symmetric equation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F3+=+%28y%2B1%29%2F-1+=+%28z-3%29%2F3 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F3+=+%28y%2B1%29%2F-1+=+%28z-3%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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