document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161537>Question 161537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If // v //  = 2, what is //-4v//? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119144 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=119144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=ai%2Bbj ALIGN=MIDDLE  ALT=\"v=ai%2Bbj\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since ||v||=2, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29=2 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4v ALIGN=MIDDLE  ALT=\"-4v\"   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=v=ai%2Bbj ALIGN=MIDDLE  ALT=\"v=ai%2Bbj\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given vector\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4v=-4%28ai%2Bbj%29 ALIGN=MIDDLE  ALT=\"-4v=-4%28ai%2Bbj%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4v=-4ai-4bj%29 ALIGN=MIDDLE  ALT=\"-4v=-4ai-4bj%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So this means:\r<BR>\n" );
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document.write( "||-4v||=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-4a%29%5E2%2B%28-4b%29%5E2%29=sqrt%2816a%5E2%2B16b%5E2%29=sqrt%2816%28a%5E2%2Bb%5E2%29%29=sqrt%2816%29%2Asqrt%28a%5E2%2Bb%5E2%29=4%2Asqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=4||v||\r<BR>\n" );
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document.write( "So this shows us that the length of ||-4v|| is simply 4 times that of ||v||. So the length of ||-4v|| is 8 units\r<BR>\n" );
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document.write( "In other words, ||-4v||=8\r<BR>\n" );
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