document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436449>Question 436449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider only vectors in R^3<BR>\n" );
document.write( "Proof: if v dot w = 0 for all v, then w = 0 <BR>\n" );
document.write( "Please help, i tried through a counterexample and my professor didn't like it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301971 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It follows from the hypothesis that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2Aw+=+abs%28w%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"w%2Aw+=+abs%28w%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28w%29+=+0 ALIGN=MIDDLE  ALT=\"abs%28w%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Only one vector has 0 magnitude, and that is the zero vector.  Hence w is the zero vector. </SPAN>\n" );
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