document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076191>Question 1076191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please find the projection of u = <6, 7> onto v = <-5, -1>. Put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+U+ ALIGN=MIDDLE  ALT=\"+U+\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the sum of two orthogonal vectors.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690959 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=690959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So the scalar projection of u onto v is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%28v%2Au%29%2Fabs%28v%29=%286%28-5%29%2B7%28-1%29%29%2Fsqrt%285%5E2%2B1%5E2%29=%28-30-7%29%2Fsqrt%2826%29=-37%2Fsqrt%2826%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now just multiply by the unit vector in the v direction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bunit%5D ALIGN=MIDDLE  ALT=\"V%5Bunit%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Fsqrt%2826%29 ALIGN=MIDDLE  ALT=\"-5%2Fsqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fsqrt%2826%29 ALIGN=MIDDLE  ALT=\"-1%2Fsqrt%2826%29\"   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=u%5Bv%5D ALIGN=MIDDLE  ALT=\"u%5Bv%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-37%2Fsqrt%2826%29%29%28-5%2Fsqrt%2826%29%29 ALIGN=MIDDLE  ALT=\"%28-37%2Fsqrt%2826%29%29%28-5%2Fsqrt%2826%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-37%2Fsqrt%2826%29%29%28-1%2Fsqrt%2826%29%29 ALIGN=MIDDLE  ALT=\"%28-37%2Fsqrt%2826%29%29%28-1%2Fsqrt%2826%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5Bv%5D ALIGN=MIDDLE  ALT=\"u%5Bv%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=185%2F26 ALIGN=MIDDLE  ALT=\"185%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F26 ALIGN=MIDDLE  ALT=\"37%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "u=6(1,0)+7(0,1)<BR>\n" );
document.write( "(1,0) and (0,1) are orthogonal since their dot product equals zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A0%2B0%2A1=0 ALIGN=MIDDLE  ALT=\"1%2A0%2B0%2A1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );