document.write( "Question 206413: Hi all, I was hoping someone could show me how to solve the following,
\n" ); document.write( "Find the equation of the line that contains points (2,1,-3) and (-1,4,1)
\n" ); document.write( "Help with steps on how to solve would be great,
\n" ); document.write( "Thanks, -nick. \n" ); document.write( "

Algebra.Com's Answer #155970 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I did this problem for you recently, Nick.  Here it is again.\r\n" );
document.write( "Is there something about it that you didn't understand about\r\n" );
document.write( "lines in space?  Would you understand it better if I used\r\n" );
document.write( "the i,j,k notation instead of the ‹a,b,c› notation? \r\n" );
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document.write( "If you need further help, you may email me at AnlytcPhil@aol.com\r\n" );
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document.write( "A line parallel to the vector v = ‹a,b,c› and passing through the\r\n" );
document.write( "point P(,,) is represented by the\r\n" );
document.write( "parametric equations\r\n" );
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document.write( ", , \r\n" );
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document.write( "or as the symmetric equations:\r\n" );
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document.write( "if none of a,b, or c are 0.\r\n" );
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document.write( "Begin by using the points P(2,1,-3) and Q(-1,4,1) \r\n" );
document.write( "to find a direction vector for the line passing through \r\n" );
document.write( "P and Q, given by\r\n" );
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document.write( "v = PQ = ‹-1-(2),4-1,1-(-3)› = ‹-3,3,4›\r\n" );
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document.write( "So we substitute in \r\n" );
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document.write( ", , \r\n" );
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document.write( "with ‹a,b,c› = ‹-3,3,4›  and the point P(,,) = P(2,1,-3)\r\n" );
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document.write( ", , \r\n" );
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document.write( "That's the parametric equations for the line.\r\n" );
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document.write( "If you want the symmetric equation of the line, we\r\n" );
document.write( "substitute in\r\n" );
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document.write( "Edwin

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