document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132778>Question 1132778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vector projection of u onto v. Then write u as the sum of two orthogonal​ vectors, one of which is proj (Subscript v)u.\r<BR>\n" );
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document.write( "u=<2​,8>, v= <4​, -5>\r<BR>\n" );
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document.write( "proj (Subscript v)u= <-128/41, 160/41>\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749902 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >>, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2 ALIGN=MIDDLE  ALT=\"proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Av=+8+-40=-32 ALIGN=MIDDLE  ALT=\"u%2Av=+8+-40=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28abs%28u%29%29%5E2=%28sqrt%284%5E2%2B5%5E2%29%29%5E2=%28sqrt%2841%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28abs%28u%29%29%5E2=%28sqrt%284%5E2%2B5%5E2%29%29%5E2=%28sqrt%2841%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2 ALIGN=MIDDLE  ALT=\"proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proj%5Bv%5Du ALIGN=MIDDLE  ALT=\"proj%5Bv%5Du\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32%2F%28sqrt%2841%29%29%5E2 ALIGN=MIDDLE  ALT=\"-32%2F%28sqrt%2841%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proj%5Bv%5Du ALIGN=MIDDLE  ALT=\"proj%5Bv%5Du\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32%2F41 ALIGN=MIDDLE  ALT=\"-32%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" >)*<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+ ALIGN=MIDDLE  ALT=\"4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >>\r<BR>\n" );
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document.write( "proj[v]u=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2832%2F41%29%2A4 ALIGN=MIDDLE  ALT=\"-%2832%2F41%29%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2832%2F41%29%28-5%29 ALIGN=MIDDLE  ALT=\"-%2832%2F41%29%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proj%5Bv%5Du ALIGN=MIDDLE  ALT=\"proj%5Bv%5Du\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128%2F41 ALIGN=MIDDLE  ALT=\"-128%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2F41 ALIGN=MIDDLE  ALT=\"160%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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