document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88102>Question 88102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the magnitude of the following vector:<BR>\n" );
document.write( "v=3i-2j </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63947 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=63947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the norm of the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\v{v}=3i-2j}\"> use the following formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left|\left|\v{v}\right|\right|=sqrt{\v{v}\bullet\v{v}}\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large {\v{v}\bullet\v{v}}\"> is the dot product of the given vector with itself\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{\v{v}\bullet\v{v}}=sqrt{(3)*(3)+(-2)*(-2)}\"> Calculate the dot product of the radicand\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{9+4}\"> Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{13}\"> Add\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left|3i-2j\right|=sqrt{13}\">\r<BR>\n" );
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document.write( "Notice if we draw the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\v{v}=3i-2j}\">  we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-5%2B2%2C+5%2B2%2C+-5%2B2%2C+5%2B2%2C%0D%0Agraph%28500%2C+500%2C+-5%2B2%2C+5%2B2%2C+-5%2B2%2C+5%2B2%2C+0%29%2C%0D%0Agreen%28line%280%2C0%2C3%2C0%29%29%2C%0D%0Agreen%28line%283%2C0%2C3%2C-2%29%29%2C%0D%0Aarrow%280%2C0%2C3%2C-2%29%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plot of the vector (black line) with the vector components (green)\r<BR>\n" );
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document.write( "and if we used Pythagorean's Theorem, we would find that the magnitude is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{13}\"> </SPAN>\n" );
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