document.write( "Question 651090: Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4). Also what point on that line is closest to the point (3,5,-4) \n" ); document.write( "
Algebra.Com's Answer #407566 by Edwin McCravy(20060)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4).
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document.write( "The distance between a point Q and a line in space is given by the formula\r\n" );
document.write( "           ‖PQ×u‖\r\n" );
document.write( "      D =  ------ \r\n" );
document.write( "            ‖u‖\r\n" );
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document.write( "where u is the direction vector for the line and P is a point on the line.\r\n" );
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document.write( "First we find PQ×u where Q(3,5,-4) and we'll\r\n" );
document.write( "take P(5,2,7) and \r\n" );
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document.write( "PQ×u = < 5-3,2-5,7-(-4) > = < 2,-3,11 > \r\n" );
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document.write( "Next we use the points (5,2,7) and (-3,6,4) to find a direction vector u for the line.\r\n" );
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document.write( "u = < -3-5,6-2,4-7 > = < -8,4,-3 >\r\n" );
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document.write( "edwin
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