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 ABCD, but it is not a rectangle.

Answer 1

Given points are A (1, 2, 3), B (-1, -2, -1), C (2, 3, 2) and D (4, 7, 6). 

To show ABCD is a parallelogram we need to show opposite sides are equal. By distance formula, we have

Since, AB = CD and BC = DA. ABCD is a parallelogram. 

Now, it is required to prove that ABCD is not a rectangle. 

For this, we show that diagonals AC and BD are unequal.