document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114535>Question 1114535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Unit vector which are perpendicular to vector 2i - j - 3k and lie in the plane of vector 7i - j - k and i + 5j - 3k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729948 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A=(2,-1,-3), B=(7,-1,-1), C=(1,5,-3)<BR>\n" );
document.write( "Find D that is coplanar to B and C and also perpendicular to A.<BR>\n" );
document.write( "Coplanar means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=p%2AB%2Bq%2AC ALIGN=MIDDLE  ALT=\"D=p%2AB%2Bq%2AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > are two scalars.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Perpendicular means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2AD=0 ALIGN=MIDDLE  ALT=\"A%2AD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A%28pB%2BqC%29=0 ALIGN=MIDDLE  ALT=\"A%2A%28pB%2BqC%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%287p%2Bq%29%2B%28-1%29%28-p%2B5q%29%2B%28-3%29%28-p-3q%29=0 ALIGN=MIDDLE  ALT=\"2%287p%2Bq%29%2B%28-1%29%28-p%2B5q%29%2B%28-3%29%28-p-3q%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814p%2B2q%29%2B%28p-5q%29%2B%283p%2B9q%29=0 ALIGN=MIDDLE  ALT=\"%2814p%2B2q%29%2B%28p-5q%29%2B%283p%2B9q%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18p%2B6q=0 ALIGN=MIDDLE  ALT=\"18p%2B6q=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3p%2Bq=0 ALIGN=MIDDLE  ALT=\"3p%2Bq=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=-3p ALIGN=MIDDLE  ALT=\"q=-3p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=p%2AB-3p%2AC ALIGN=MIDDLE  ALT=\"D=p%2AB-3p%2AC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D=p(2,-1,-3)-3p(1,5,-3)<BR>\n" );
document.write( "D=(2p,-p,-3p)+(-3p,-15p,9p)<BR>\n" );
document.write( "D=(-p,-16p,6p)<BR>\n" );
document.write( "To find the unit vector, divide by the magnitude of the vector,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28D%29=sqrt%28%28-p%29%5E2%2B%28-16p%29%5E2%2B%286p%29%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28D%29=sqrt%28%28-p%29%5E2%2B%28-16p%29%5E2%2B%286p%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28D%29=sqrt%28p%5E2%2B256p%5E2%2B36p%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28D%29=sqrt%28p%5E2%2B256p%5E2%2B36p%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28D%29=sqrt%28293p%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28D%29=sqrt%28293p%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28D%29=sqrt%28293%29p ALIGN=MIDDLE  ALT=\"abs%28D%29=sqrt%28293%29p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bu%5D=D%2Fabs%28D%29 ALIGN=MIDDLE  ALT=\"D%5Bu%5D=D%2Fabs%28D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bu%5D ALIGN=MIDDLE  ALT=\"D%5Bu%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%2F%28sqrt%28293%29p%29 ALIGN=MIDDLE  ALT=\"-p%2F%28sqrt%28293%29p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16p%29%2F%28sqrt%28293%29p%29 ALIGN=MIDDLE  ALT=\"%28-16p%29%2F%28sqrt%28293%29p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286p%29%2F%28sqrt%28293%29p%29 ALIGN=MIDDLE  ALT=\"%286p%29%2F%28sqrt%28293%29p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bu%5D ALIGN=MIDDLE  ALT=\"D%5Bu%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28sqrt%28293%29%29 ALIGN=MIDDLE  ALT=\"-1%2F%28sqrt%28293%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2F%28sqrt%28293%29%29 ALIGN=MIDDLE  ALT=\"-16%2F%28sqrt%28293%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28sqrt%28293%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28sqrt%28293%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );