document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31236>Question 31236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> vector A=3i+4j is a vector in xy plane,<BR>\n" );
document.write( "vector B is a vector perpendicular to vector A,<BR>\n" );
document.write( "what will be the vector C equal to,which has projections 1 and 2 along vectors A and B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17902 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if vector B is perpendicular to vector A and A is solely in the x-y plane then vector B has to be solely in the z-plane, so its vector is B=ck...some value of k... we do not know where in the z-plane it lies.\r<BR>\n" );
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document.write( "So, C = 3i+4j+ck\r<BR>\n" );
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document.write( "I think this is what you require.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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document.write( "OK, after your reply, B is also in the xy plane: my mistake, sorry.\r<BR>\n" );
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document.write( "OK, in the xy plane, a.b = 0 for 2 orthogonal vectors.\r<BR>\n" );
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document.write( "we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C+3%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C+3%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C+x%2Cy%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C+x%2Cy%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0\r<BR>\n" );
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document.write( "so, 3x+4y=0\r<BR>\n" );
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document.write( "Now, if both terms were 12 and one negative, then we would have zero. So, how about x=4 and y=-3... that would equal zero.\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C+3%2C4%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C+3%2C4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C4%2C-3%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C4%2C-3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 holds true\r<BR>\n" );
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document.write( "So, C = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C+3%2C4%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C+3%2C4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C4%2C-3%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C4%2C-3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C%283%2B4%29%2C%284-3%29%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C%283%2B4%29%2C%284-3%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C7%2C1%29+%29 ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C7%2C1%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is one version of the answer, since the scalar product could also have been: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C+3%2C4%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C+3%2C4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C-4%2C3%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C-4%2C3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0\r<BR>\n" );
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document.write( "in which case, B would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C-4%2C3%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C-4%2C3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. And hence C would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C%283-4%29%2C%284%2B3%29%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C%283-4%29%2C%284%2B3%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28matrix%282%2C1%2C-1%2C7%29%29+ ALIGN=MIDDLE  ALT=\"+%28matrix%282%2C1%2C-1%2C7%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "either is correct.<BR>\n" );
document.write( "Jon<BR>\n" );
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