document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168322>Question 168322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can anyone help with the following assignment question, \r<BR>\n" );
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document.write( "Two aircrafts take off simultaneously from different airports. As they climb, their positions relative to an air traffic control centre t minutes later are given by the vectors:<BR>\n" );
document.write( "r1 = 4i-30j +t(8i+2j+0.3k)<BR>\n" );
document.write( "r2 = 12i+26j+ t(6i-3j+0.8k)<BR>\n" );
document.write( "where i direction is due east, the j is due north and k is vertical distance and the units are kilometres. \r<BR>\n" );
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document.write( "a) find the coordinates of the point over the groun where the two planes cross<BR>\n" );
document.write( "b) find also the difference in height and time that they both pass this point. \r<BR>\n" );
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document.write( "this is a completely different question to the examples we have done in the handouts and lessons so i am really struggling with this. \r<BR>\n" );
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document.write( "kevin  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124084 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=124084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, let's break down the positions of each.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1+=+4i-30j+%2Bt%288i%2B2j%2B0.3k%29 ALIGN=MIDDLE  ALT=\"r1+=+4i-30j+%2Bt%288i%2B2j%2B0.3k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1=4i-30j%2B8ti%2B2tj%2B0.3tk ALIGN=MIDDLE  ALT=\"r1=4i-30j%2B8ti%2B2tj%2B0.3tk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1=%284%2B8t%29i%2B%28-30%2B2t%29j%2B0.3tk ALIGN=MIDDLE  ALT=\"r1=%284%2B8t%29i%2B%28-30%2B2t%29j%2B0.3tk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and similarly,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r2+=+12i%2B26j%2B+t%286i-3j%2B0.8k%29 ALIGN=MIDDLE  ALT=\"r2+=+12i%2B26j%2B+t%286i-3j%2B0.8k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r2=12i%2B26j%2B6ti-3tj%2B0.8tk ALIGN=MIDDLE  ALT=\"r2=12i%2B26j%2B6ti-3tj%2B0.8tk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r2=%2812%2B6t%29i%2B%2826-3t%29j%2B0.8tk ALIGN=MIDDLE  ALT=\"r2=%2812%2B6t%29i%2B%2826-3t%29j%2B0.8tk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you have the position of both planes as a function of t.<BR>\n" );
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document.write( "When the planes cross, their i and j coordinates will be the same. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1%5Bi%5D=r2%5Bi%5D ALIGN=MIDDLE  ALT=\"r1%5Bi%5D=r2%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B8t=12%2B6t ALIGN=MIDDLE  ALT=\"4%2B8t=12%2B6t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t=8 ALIGN=MIDDLE  ALT=\"2t=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1%5Bj%5D=r2%5Bj%5D ALIGN=MIDDLE  ALT=\"r1%5Bj%5D=r2%5Bj%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30%2B2t=26-3t ALIGN=MIDDLE  ALT=\"-30%2B2t=26-3t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t=56 ALIGN=MIDDLE  ALT=\"5t=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=56%2F5 ALIGN=MIDDLE  ALT=\"t=56%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "There is a problem. <BR>\n" );
document.write( "For them to pass the same i,j point, the times need to match. <BR>\n" );
document.write( "When t=4,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1x=r2x=36 ALIGN=MIDDLE  ALT=\"r1x=r2x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r1y=-30%2B2t=-30%2B8=-22 ALIGN=MIDDLE  ALT=\"r1y=-30%2B2t=-30%2B8=-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and similarly,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r2y=26-3t=26-12=14 ALIGN=MIDDLE  ALT=\"r2y=26-3t=26-12=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As you can see the x coordinates match, the y-coordinates don't. <BR>\n" );
document.write( "The same thing happens at t=56/5.<BR>\n" );
document.write( "There is no point in time when \"i\" positions and \"j\" positions match for the planes. <BR>\n" );
document.write( "Please re-check the numbers and re-post. <BR>\n" );
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