Show that the points A(1, 2, 3), B(-1, -2, -1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram. Show that ABCD is not a rectangle.
To prove: Points A, B, C, D form parallelogram.
Formula:
The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D=
Here,
(x1,y1,z1)= (1, 2, 3)
(x2,y2,z2)= (-1, -2, -1)
(x3,y3,z3)= (2, 3, 2)
(x4,y4,z4)= (4, 7, 6)
Length AB = 
= 
= 
= 
= 
Length BC = 
= 
= 
= 
= 
Length CD = 
= 
= 
= 
= 
Length AD = 
= 
= 
= 
= 
Length AC = 
= 
= 
= 
= 
Length BD = 
= 
= 
= 
= 
Here, AB = CD which are opposite sides of polygon.
BC = AD which are opposite sides of polygon.
Also the diagonals AC and BD are not equal in length.
Hence, the polygon is not a rectangle.
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