document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=417490>Question 417490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three vectors a,b and c are such that  a.(b+c)=b.(a+c)\r<BR>\n" );
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document.write( "Show that c must be perpendicular to a-b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #292311 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=292311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We only need to show that c.(a-b) = 0 or (a-b).c = 0\r<BR>\n" );
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document.write( "a.(b+c)=b.(a+c) \r<BR>\n" );
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document.write( "a.b+a.c = b.a + b.c\r<BR>\n" );
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document.write( "a.b+a.c = a.b + b.c\r<BR>\n" );
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document.write( "a.b+a.c-a.b = a.b + b.c - a.b\r<BR>\n" );
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document.write( "(a.b-a.b)+a.c = (a.b- a.b) + b.c \r<BR>\n" );
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document.write( "0+a.c = 0 + b.c \r<BR>\n" );
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document.write( "a.c = b.c\r<BR>\n" );
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document.write( "a.c - b.c = 0\r<BR>\n" );
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document.write( "(a-b).c = 0\r<BR>\n" );
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document.write( "Therefore, c is perpendicular to a-b\r<BR>\n" );
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document.write( "Note: you can draw a picture to accompany the proof, but don't rely exclusively on it (as it may not be drawn correctly)\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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