Question

The points (5, – 4, 2), (4, –3, 1), (7, – 6, 4) and (8, –7, 5) are the vertices of [RPET 2002]

• A. A rectangle
• B. A square
• C. A parallelogram
• D. None of these

Answer 1

The correct option is D

None of these

Let A(5, -4, 2), B(4, =3, 1), C(7, -6, 4)
and $D(8,-7,5).ThenAB=\sqrt{1+1+1}=\sqrt{3},$
BC = $\sqrt{9+9+9}=3\sqrt{3},CD=\sqrt{1+1+1}=\sqrt{3}$
AD = $\sqrt{9+9+9}=3\sqrt{3}.$
But $\overrightarrow{AB}.\overrightarrow{BC}\ne 0$
Let the angle between AB and BC be $\theta ,$ then cos $\theta =-1\Rightarrow \theta =\pi .$