document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976985>Question 976985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the unit vector directed oppositely to the vector <-4i + j + 4k>?\r<BR>\n" );
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document.write( "(My approach was to find the unit vector first, then reverse the signs. is this correct?)\r<BR>\n" );
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document.write( "Thank you for your time and help!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598479 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=598479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your approach is correct. You can also reverse the signs, then find the unit vector. It doesn't matter either way.\r<BR>\n" );
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document.write( "Magnitude of vector\r<BR>\n" );
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document.write( "v = -4i + j + 4k\r<BR>\n" );
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document.write( "|v| = sqrt(a^2 + b^2 + c^2)<BR>\n" );
document.write( "|v| = sqrt((-4)^2 + (1)^2 + (4)^2)<BR>\n" );
document.write( "|v| = sqrt(33)<BR>\n" );
document.write( "|v| = 5.74456264653802\r<BR>\n" );
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document.write( "Divide each component by the magnitude\r<BR>\n" );
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document.write( "-4/5.74456264653802 = -0.6963106238228<BR>\n" );
document.write( "1/5.74456264653802 = 0.1740776559557<BR>\n" );
document.write( "4/5.74456264653802 = 0.6963106238228\r<BR>\n" );
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document.write( "The unit vector is -0.6963106238228i + 0.1740776559557j + 0.6963106238228k\r<BR>\n" );
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document.write( "Flip the signs: 0.6963106238228i - 0.1740776559557j - 0.6963106238228k\r<BR>\n" );
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document.write( "This final answer is approximate. If you want the exact answer in terms of radicals, use sqrt(33) in place of 5.74456264653802\r<BR>\n" );
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document.write( "So the exact answer would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Fsqrt%2833%29%29i+-+%281%2Fsqrt%2833%29%29j+-+%284%2Fsqrt%2833%29%29k ALIGN=MIDDLE  ALT=\"%284%2Fsqrt%2833%29%29i+-+%281%2Fsqrt%2833%29%29j+-+%284%2Fsqrt%2833%29%29k\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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