show that the quadrilateral with vertices at the following points is a parallelogram and find its area. a = (5,2,0), b = (2,6,1), c = (2,4,7), d = (5,0,6)

Answer 1

AB has direction (-3,4,1)
BC has direction (0,-2,6)
CD has direction (3,-4,-1)
DA has direction (0,-2,6)

So, AB || CD
and BC || AD

since the sides are parallel in pairs, they must have the same lengths in pairs (I trust you can verify this).

the area is just
|(b-a)x(d-a)|
where a,b,c,d are the vectors to the points A,B,C,D.

Answer 2

thanks steve. u really help me out.. really appreciate it .. =)