document.write( "Question 328183: If ABCD is a parallelogram with A(2,1,4), B(1,4,3) and C(1,0,2), find:
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Algebra.Com's Answer #235059 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Since A is the point (2,1,4) and B is the point (1,4,3), the vector from A to B\r\n" );
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document.write( "< 1-2, 4-1, 3-4 > or < -1, 3, -1 >\r\n" );
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document.write( "Since B is the point (1,4,3) and C is the point (1,0,2), the vector from B to C\r\n" );
document.write( "is \r\n" );
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document.write( "< 1-1, 0-4, 2-3 > or < 0, -4, -1 >\r\n" );
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document.write( "Since those vectors are adjacent sides of a parallelogram, the\r\n" );
document.write( "area of the parallelogram is the magnitude of their cross\r\n" );
document.write( "product. So we find their cross product:\r\n" );
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document.write( " = (-3-4)i - (1-0)j + (4-0)k = -7i - j +4k\r\n" );
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document.write( "And the magnitude of their cross product is \r\n" );
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document.write( "\"sqrt%28%28-7%29%5E2%2B%28-1%29%5E2%2B%284%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%2849%2B1%2B16%29\"\"%22%22=%22%22\"\"sqrt%2866%29\"\r\n" );
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document.write( "(b)\r\n" );
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document.write( "Let D be the point (x1, y1, z1).  Since A is the point (2,1,4),\r\n" );
document.write( "then the vector from A to D is < x1-2, y1-1, z1-4 >\r\n" );
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document.write( "Since C is the point (1,0,2) and B is the point (1,4,3),\r\n" );
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document.write( "the vector from B to C is < 1-1, 0-4, 2-3 > or < 0, -4, -1 >\r\n" );
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document.write( "Since opposite sides of a parallelogram are equal and parallel,\r\n" );
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document.write( "they must be the same vector.  Therefore we set the corresponding\r\n" );
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document.write( "components  of the vector from A to D,  < x1-2, y1-1, z1-4 > and the vector from B to C < 0,-4,-1 >\r\n" );
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document.write( "equal:\r\n" );
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document.write( "x1-2 = 0, y1-1 = -4, z1-4 = -1,\r\n" );
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document.write( "so\r\n" );
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document.write( "x1=2, y1=-3, z1=3\r\n" );
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document.write( "and the point D is (x1, y1, z1) = (2,-3,3)\r\n" );
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document.write( "Edwin
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