document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286948>Question 286948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let vector v=<5,-1,4>. Give a vector w in the opposite direction of v and with magnitude twelve. Give its components to the nearest tenth. I don't understand how to solve the problem and I can't seem to find any similar examples in the text. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208093 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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/cgi-bin/show-face.mpl?user=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to get the opposite direction, change the signs of the components\r<BR>\n" );
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document.write( "w = <-5k, 1k, -4k>\r<BR>\n" );
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document.write( "the \"k\" is the factor to make the magnitude of w equal 12\r<BR>\n" );
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document.write( "the magnitude is the length of the vector<BR>\n" );
document.write( "___ found by using the Pythagorean theorem on the components<BR>\n" );
document.write( "___ m^2 = x^2 + y^2 + z^2\r<BR>\n" );
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document.write( "144 = 25k^2 + k^2 + 16k^2 = 42k^2\r<BR>\n" );
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document.write( "k = sqrt(144/42) = 1.852 (approx)\r<BR>\n" );
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document.write( "plug in the value of k to find the components of w </SPAN>\n" );
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