document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88187>Question 88187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the magnitude of the following vector: v=4i-2j </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64029 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=64029\">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 \v{v}=4i-2j\"> use the following formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left|\left|\v{a}\right|\right|=sqrt{\v{a}\bullet\v{a}}\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large {\v{a}\bullet\v{a}}\"> is the dot product of the given vector with itself\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember the dot product of the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \v{a}\"> with itself is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \v{a}\bullet\v{a}= (a_{0})*(a_{0})+(a_{1})*(a_{1})\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{\v{a}\bullet\v{a}}=sqrt{(4)*(4)+(-2)*(-2)}\"> Calculate the dot product of the radicand\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{16+4}\"> Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{20}\"> Add\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2sqrt{5}\"> Simplify if possible\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left|4i-2j\right|=2sqrt{5}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "Lets use Pythagorean's Theorem to check our work\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice if we draw the vector <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \v{v}=4i-2j\"> we get\r<BR>\n" );
document.write( "\n" );
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%2C4%2C0%29%29%2C%0D%0Agreen%28line%284%2C0%2C4%2C-2%29%29%2C%0D%0Aarrow%280%2C0%2C4%2C-2%29%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" );
document.write( "\n" );
document.write( "We can see that the vector has x and y components, which form the legs of the triangle. We can also see that the legs are 4 units and 2 units\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we have a triangle with legs of 4 , 2 and a hypotenuse of x(our unknown side), we can use Pythagoreans theorem to find the unknown side.\r<BR>\n" );
document.write( "\n" );
document.write( "Pythagoreans theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2%2B2%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"4%5E2%2B2%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in a=4 and b=2 and lets solve for c\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+6+%2B+4+=++c++%5E+2 ALIGN=MIDDLE  ALT=\"1+6+%2B+4+=++c++%5E+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each individual term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+0+=++c++%5E+2 ALIGN=MIDDLE  ALT=\"2+0+=++c++%5E+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+q+r+t+%28+2+0+%29+=+s+q+r+t+%28++c++%5E+2+%29 ALIGN=MIDDLE  ALT=\"s+q+r+t+%28+2+0+%29+=+s+q+r+t+%28++c++%5E+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29=c ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the length of the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This verifies our answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );