Show that the points A(1,2,3), B(-1,-2,-1), C(2,3,2), D(4,7,6) are the vertices of a parallelogram.

Explanation

Here, we are given vertices, `A(1,2,3), B(-1,-2,-1),C(2,3,2),D(4,7,6)`.
With the given vertices,

`AB = sqrt((-2)^2+(-4)^2+(-4)^2 ) = sqrt(4+16+16) = sqrt 36 = 6`

`BC = sqrt((3)^2+(5)^2+(3)^2 ) = sqrt(9+25+9) = sqrt 43 `

`CD = sqrt((2)^2+(4)^2+(4)^2 ) = sqrt(4+16+16) = sqrt 36 = 6`

`AD = sqrt((3)^2+(5)^2+(3)^2 ) = sqrt(9+25+9) = sqrt 43 `

Here, `AB = CD` and `BC = AD`.

So, `ABCD` can be a parallelogram or a rectangle.

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