document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165567>Question 165567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find a unit vector along each of the following vectors;<BR>\n" );
document.write( "(i) r=3i^+4j^     (ii)r=12i^-5j^  (iii)r=-2i^-2j^-5k^  (iv)r=i^+2j^+3k^ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122049 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the unit vector in the direction of the given vector, divide the vector by its magnitude,M.<BR>\n" );
document.write( "This way it has the same direction and magnitude of 1.<BR>\n" );
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document.write( "i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3i%2B4j ALIGN=MIDDLE  ALT=\"r=3i%2B4j\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Br%5D=sqrt%283%5E2%2B4%5E2%29=sqrt%289%2B16%29=sqrt%2825%29=5 ALIGN=MIDDLE  ALT=\"M%5Br%5D=sqrt%283%5E2%2B4%5E2%29=sqrt%289%2B16%29=sqrt%2825%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bu%5D=%283%2F5%29i%2B%284%2F5%29j ALIGN=MIDDLE  ALT=\"r%5Bu%5D=%283%2F5%29i%2B%284%2F5%29j\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=12i-5j ALIGN=MIDDLE  ALT=\"r=12i-5j\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Br%5D=sqrt%2812%5E2%2B5%5E2%29=sqrt%28144%2B25%29=sqrt%28169%29=13 ALIGN=MIDDLE  ALT=\"M%5Br%5D=sqrt%2812%5E2%2B5%5E2%29=sqrt%28144%2B25%29=sqrt%28169%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bu%5D=%2812%2F13%29i%2B%28-5%2F13%29j ALIGN=MIDDLE  ALT=\"r%5Bu%5D=%2812%2F13%29i%2B%28-5%2F13%29j\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-2i-2j-5k ALIGN=MIDDLE  ALT=\"r=-2i-2j-5k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Br%5D=sqrt%282%5E2%2B2%5E2%2B5%5E2%29=sqrt%284%2B4%2B25%29=sqrt%2833%29 ALIGN=MIDDLE  ALT=\"M%5Br%5D=sqrt%282%5E2%2B2%5E2%2B5%5E2%29=sqrt%284%2B4%2B25%29=sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bu%5D=%28-2%2Fsqrt%2833%29%29i%2B%28-2%2Fsqrt%2833%29%29j%2B%285%2Fsqrt%2833%29%29k ALIGN=MIDDLE  ALT=\"r%5Bu%5D=%28-2%2Fsqrt%2833%29%29i%2B%28-2%2Fsqrt%2833%29%29j%2B%285%2Fsqrt%2833%29%29k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=i%2B2j%2B3k ALIGN=MIDDLE  ALT=\"r=i%2B2j%2B3k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5Br%5D=sqrt%281%5E2%2B2%5E2%2B3%5E2%29=sqrt%281%2B4%2B9%29=sqrt%2814%29 ALIGN=MIDDLE  ALT=\"M%5Br%5D=sqrt%281%5E2%2B2%5E2%2B3%5E2%29=sqrt%281%2B4%2B9%29=sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bu%5D=%281%2Fsqrt%2814%29%29i%2B%282%2Fsqrt%2814%29%29j%2B%283%2Fsqrt%2814%29%29k ALIGN=MIDDLE  ALT=\"r%5Bu%5D=%281%2Fsqrt%2814%29%29i%2B%282%2Fsqrt%2814%29%29j%2B%283%2Fsqrt%2814%29%29k\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );