document.write( "Question 656152: find if the points joining A(6,7,1), B(2,-3,1) and C(4,-5,1) are collinear. \n" ); document.write( "

Algebra.Com's Answer #409367 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We need to find whether the vector AC is a multiple of the vector AB\r\n" );
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document.write( "AC = < 4-6, -5-7, 1-1 > = < -2, -12, 0 > \r\n" );
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document.write( "AB = < 2-6, -3-7, 1-1 > = < -4, -10, 0 >\r\n" );
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document.write( "AC is not a multiple of AB, so A,B, and C are not collinear.\r\n" );
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document.write( "You can also do it by finding the distances between the three points,\r\n" );
document.write( "and determining whether the sum of two of the distances AB, BC, AC are\r\n" );
document.write( "equal to the third distance:\r\n" );
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document.write( "AB =  =  =  =  =  = \r\n" );
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document.write( "AC =  =  =  =  =  = \r\n" );
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document.write( "BC =  =  =  =  =  =  = \r\n" );
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document.write( "No two of those have the sum of the smallest two,  +  \r\n" );
document.write( "does not equal the largest , so the three points cannot be\r\n" );
document.write( "collinear. \r\n" );
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document.write( "Edwin

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