document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201856>Question 1201856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 'Lines in 3-Space' lesson:\r<BR>\n" );
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document.write( "1. State where possible vector, parametric, and symmetric equations for each of the following lines. \r<BR>\n" );
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document.write( "a. The line passing through the point P (-1,2,1) with direction vector (3,-2,1)\r<BR>\n" );
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document.write( "b. The line passing through the point B (-2,3,0) and parallel to the line passing through the points M (-2,-2,1) and N (-2,4,7)\r<BR>\n" );
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document.write( "c.The line passing through the points Q (1,2,4) and parallel to the z-axis  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836396 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "State where possible vector, parametric, and symmetric equations for each of the following lines.<BR>\n" );
document.write( "a. The line passing through the point P (-1,2,1) with direction vector (3,-2,1)<BR>\n" );
document.write( "b. The line passing through the point B (-2,3,0) and parallel to the line passing through the <BR>\n" );
document.write( "   points M(-2,-2,1) and N(-2,4,7)<BR>\n" );
document.write( "c. The line passing through the points Q (1,2,4) and parallel to the z-axis<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  Parametric equation is\r\n" );
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document.write( "        (x,y,z) = (-1,2,1) + t*(3,-2,1),  where t is any real number.\r\n" );
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document.write( "     From the formula, it is immediately seen that the point P lies in this line (at t= 0),\r\n" );
document.write( "                                          and that the direction vector is (3,-2,1).\r\n" );
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document.write( "     In vector form, this parametric equation is the set of these three scalar (component) equations\r\n" );
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document.write( "         x = -1 + 3t,  y = 2 - 2t,  z = 1 + t.\r\n" );
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document.write( "(b)  The direction vector for this line is vector MN connecting the points \r\n" );
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document.write( "         MN = N_bar - M_bar = (-2,4,7) - (-2,-2,1) = (0,6,6).\r\n" );
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document.write( "     Hence, similar to (a), the parametric equation of the desired line is \r\n" );
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document.write( "         (x,y,z) = (-2,3,0) + t*(0,6,6),  where t is any real number.\r\n" );
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document.write( "     In vector form, this parametric equation is the set of these three scalar (component) equations\r\n" );
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document.write( "         x = -2,  y = 3 + 6t,  z = 6t.\r\n" );
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document.write( "(c)  The line passing through the points Q(1,2,4) and parallel to z-axis in parametric form is\r\n" );
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document.write( "        (x,y,z) = (1,2,t),  where t is any real number.\r\n" );
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document.write( "     In vector form, this parametric equation is the set of these three scalar (component) equations\r\n" );
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document.write( "         x = 1,  y = 2,  z = t. \r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "A student SHOULD be able to complete this assignment on his or her own as soon as he (or she)<BR>\n" );
document.write( "get familiar with definitions of all basic conceptions, participating in the problem's description.\r<BR>\n" );
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document.write( "Well, may be, having minimal additional training.\r<BR>\n" );
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document.write( "The solution does not require a flight of thought in higher spheres - only good understanding <BR>\n" );
document.write( "of the learned conceptions.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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