document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040746>Question 1040746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Helloo amazing tutors, can you guys help me out in answering this? Thank youu\r<BR>\n" );
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document.write( "The points A, B, C and D have position vectors 3i + 2k, 2i &#8722; 2j + 5k, 2j + 7k and &#8722;2i + 10j + 7k<BR>\n" );
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document.write( "(i) Use a scalar product to show that BA and BC are perpendicular<BR>\n" );
document.write( "(ii) Show that BC and AD are parallel and find the ratio of the length of BC to the length of AD </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655640 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the vectors are perpendicular, then the dot product equals zero.<BR>\n" );
document.write( "A=(3,0,2)<BR>\n" );
document.write( "B=(2,-2,5)<BR>\n" );
document.write( "C=(0,2,7)<BR>\n" );
document.write( "D=(-2,10,7)<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "BA=(2-3,-2-0,5-2)=(-1,-2,3)<BR>\n" );
document.write( "BC=(2-0,-2-2,5-7)=(2,-4,-2)<BR>\n" );
document.write( "The dot product is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BA%2ABC=-1%2A2%2B%28-2%29%28-4%29%2B3%28-2%29 ALIGN=MIDDLE  ALT=\"BA%2ABC=-1%2A2%2B%28-2%29%28-4%29%2B3%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete that to verify that the dot product is zero.<BR>\n" );
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document.write( "AD=(3-(-2),0-10,2-7)=(5,-10,-5)<BR>\n" );
document.write( "AD=5*(1,-2,1)<BR>\n" );
document.write( "Similarly for BC,<BR>\n" );
document.write( "BC=(2,-4,2)<BR>\n" );
document.write( "BC=2*(1,-2,1)<BR>\n" );
document.write( "So they are both multiples of the same vector and the ratios of their lengths is equal to the ratio of the multipliers,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD%2FBC=5%2F2 ALIGN=MIDDLE  ALT=\"AD%2FBC=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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