First slide
Introduction to 3-D Geometry
Question

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

Easy
Solution

Let , A(5, -4,2), B(4, - 3, 1), C(7, -6, 4) and D(8, - 7 ,5). 

Then,

AB=(45)2+(3+4)2+(12)2=1+1+1=3BC=(74)2+(6+3)2+(41)2=9+9+9=33CD=(87)2+(7+6)2+(54)2=1+1+1=3AD=(85)2+(7+4)2+(52)2=9+9+9=33AC=(75)2+(6+4)2+(42)2=4+4+4=23BD=(84)2+(7+3)2+(51)2=16+16+16=43

Here, we see that opposite sides .AB = CD,BC = AD are equal and diagonals AC≠BD
Hence, given points are the vertices of a parallelogram. 

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