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 #655639 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=655639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let O be the origin (0,0,0).<BR>\n" );
document.write( "Then vector OA = <3,0,2>,<BR>\n" );
document.write( "vector OB = <2,-2,5>,<BR>\n" );
document.write( "vector OC = <0,2,7>, and <BR>\n" );
document.write( "vector OD = <-2,10,7>.\r<BR>\n" );
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document.write( "(i)<BR>\n" );
document.write( "==> BA = OA - OB = <1,2,-3>.  Also,\r<BR>\n" );
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document.write( "BC = OC - OB = <-2,4,2> = 2<-1,2,1>.\r<BR>\n" );
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document.write( "==>BA*BC = 1*-2 + 2*4 + -3*2 = -2+8-6 = 0.\r<BR>\n" );
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document.write( "==> Vectors BA and BC are perpendicular.\r<BR>\n" );
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document.write( "(ii)<BR>\n" );
document.write( "Now AD = OD - OA = <-5,10,5> = 5<-1,2,1>.<BR>\n" );
document.write( "Since both BC and AD are non-zero multiples of the same vector <-1,2,1>,  these two vectors are parallel.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28BC%29%2Fabs%28AD%29+=+2%2F5 ALIGN=MIDDLE  ALT=\"abs%28BC%29%2Fabs%28AD%29+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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