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Show that the points A (1, 2, 3), B (1,...

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 ABCD, but it is not a rectangle.

Text Solution

Verified by Experts

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.
For `ABCD` to be a rectangle, all angles should be `90^@`.
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