document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582461>Question 582461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me. I want to know if my answer is correct. <BR>\n" );
document.write( "Which of the following is/are correct? <BR>\n" );
document.write( "My answer is none are correct because the answers are not 1 over the square roots <BR>\n" );
document.write( "A) if u = (u1, u2) with ui not equal to 0 for all 1 < or equal to i < or equal to 2... then the unit vector in the direction of u is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fsqrt%28u1%5E2+%2B+u2%5E2%29 ALIGN=MIDDLE  ALT=\"+1%2Fsqrt%28u1%5E2+%2B+u2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >(u1, u2) \r<BR>\n" );
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document.write( "B) if u = (1, 2, 3) then the unit vector in the same direction of u is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%2814%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >(1, 2, 3)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372085 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "A unit vector is represented by the vector divided by the norm of the vector, in other words, it is the vector with the magnitude (or length if you prefer) normalized to 1.\r<BR>\n" );
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document.write( "Hence, if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \mathbf{u\ =\ (u_1,\,u_2)}\">, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \mathbf{\||u\||\ =\ sqrt{u_1^{\,2}\ +\ u_2^{\,2}}}\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \mathbf{\^{u}\ =\ \frac{u}{\||u\||}}\"> which is the same thing as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \mathbf{\^{u}\ =\ \frac{u}{sqrt{u_1^{\,2}\ +\ u_2^{\,2}}}\"> and which in turn is exactly the same as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \mathbf{\^{u}\ =\ \frac{1}{sqrt{u_1^{\,2}\ +\ u_2^{\,2}}}\,\cdot\, u\">.  I can't find any fault with the given answers.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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