Question

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.

Answer 1

Apply distance formula, and find the distance between all the points:

From above result, we have

AB = CD [opposite sides]

BC = AD [opposite sides]

Diagonal AC ≠ BD, Diagonals are not equal

Hence, Points are vertices of parallelogram and ABCD is not a rectangle.