document.write( "Question 1067844: show that points (1,2,3);(-1,-2,-1);(2,3,2) and (4,7,6) are vertices of parallelogram but it is not a rectangle. \n" ); document.write( "
Algebra.Com's Answer #683063 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's an easier way.\r\n" );
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document.write( "A(1,2,3) B(-1,-2,-1); C(2,3,2) and D(4,7,6)\r\n" );
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document.write( "       →\r\n" );
document.write( "Vector AD = <4-1,7-2,6-3> = <3,5,3>\r\n" );
document.write( "       →\r\n" );
document.write( "Vector CD = <2-(-1),3-(-2),2-(-1)> = <3,5,3>\r\n" );
document.write( "                                                       →    →\r\n" );
document.write( "So sides AD and CD are both equal and parallel because AD = CD.\r\n" );
document.write( "Therefore ABCD is a parallelogram because a quadrilateral with\r\n" );
document.write( "a pair of parallel and equal sides is a parallelogram.\r\n" );
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document.write( "To prove it is not a rectangle, we find the dot product of two\r\n" );
document.write( "                                            →    \r\n" );
document.write( "adjacent sides and show it is not 0. We dot AD which is <3,5,3> with\r\n" );
document.write( "→\r\n" );
document.write( "CD = <4-2,7-3,6-2> = <2,4,4>\r\n" );
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document.write( "<3,5,3> • <2,4,4> = (3)(2)+(5)(4)+(3)(4) = 6+20+12 = 38 which\r\n" );
document.write( "is not 0.  Therefore parallelogram ABCD is not a rectangle.\r\n" );
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document.write( "Edwin
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