document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166634>Question 166634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find  // v //  if   v  =  -5 i  +  12 j <BR>\n" );
document.write( "Find the unit vector having the same direction as  v,   if   v  =  - 5 i  +  12 j  <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 #122819 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=122819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}=-5i+12j\">, this means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}=<-5,12>\">\r<BR>\n" );
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document.write( "So for any vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{z}=<a,b>\"> the magnitude or norm of that vector is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE ||\vec{z}||=\sqrt{a^2+b^2}\">\r<BR>\n" );
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document.write( "So in this case\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE ||\vec{v}||=\sqrt{(-5)^2+(12)^2}=\sqrt{25+144}=\sqrt{169}=13\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE ||\vec{v}||=13\">\r<BR>\n" );
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document.write( "Geometrically, this means that the length of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}\"> is 13 units\r<BR>\n" );
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document.write( "To find the unit vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{u}\"> that has the same direction as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}\">, simply divide EACH component of the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}\"> by the length of the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}\">.\r<BR>\n" );
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document.write( "So...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{u}=\frac{\vec{v}}{||\vec{v}||}=\frac{<-5,12>}{13}=<-\frac{5}{13},\frac{12}{13}>\">\r<BR>\n" );
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document.write( "So the unit vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{u}\"> that has the same direction as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{v}\"> is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \vec{u}=<-\frac{5}{13},\frac{12}{13}>\"> </SPAN>\n" );
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