The points (5, - 4,2),(4,- 3, 1),(7, - 6, 4) and (8, - 7 , 5) are the vertices of

Let , A(5, -4,2), B(4, - 3, 1), C(7, -6, 4) and D(8, - 7 ,5). Then,AB=(4−5)2+(−3+4)2+(1−2)2=1+1+1=3BC=(7−4)2+(−6+3)2+(4−1)2=9+9+9=33CD=(8−7)2+(−7+6)2+(5−4)2=1+1+1=3AD=(8−5)2+(−7+4)2+(5−2)2=9+9+9=33AC=(7−5)2+(−6+4)2+(4−2)2=4+4+4=23BD=(8−4)2+(−7+3)2+(5−1)2=16+16+16=43Here, we see that opposite sides .AB = CD,BC = AD are equal and diagonals AC≠BDHence, given points are the vertices of a parallelogram.