document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=413472>Question 413472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12.	Is x • x ever equal to x?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290158 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=290158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It could happen. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax+=+x ALIGN=MIDDLE  ALT=\"x%2Ax+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29+=+0 ALIGN=MIDDLE  ALT=\"x%28x-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x = 0 or 1.\r<BR>\n" );
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document.write( "However you stated the subject was \"trigonometry.\" You may be referring to the dot product of two vectors A and B. If X is a vector, then we want the dot product equal to the original vector in direction and magnitude, hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28X%29%2Aabs%28X%29%2Acos%28theta%29+=+X ALIGN=MIDDLE  ALT=\"abs%28X%29%2Aabs%28X%29%2Acos%28theta%29+=+X\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the angle in between. Since we're multiplying the same vector, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+0 ALIGN=MIDDLE  ALT=\"theta+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"cos%28theta%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It is indeed possible to have a vector such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28X%29%2Aabs%28X%29+=+X ALIGN=MIDDLE  ALT=\"abs%28X%29%2Aabs%28X%29+=+X\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which happens when X = 1i+0j or X = 0. </SPAN>\n" );
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