Question

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

vector ab = (-3,4,1)
vector dc = (3, -4, -1) = vector cd

since their magnitude is the same, and they simply have opposite direction they must be equal and parallel
So the figure is a parallogram
vector cb = (0,-2,6)

area = cross product of ab and cb
= (-3,4,1) x (0,-2,6)
= (26,18,6)
whose magnitude is √(26^2+18^2+6^) = √1036

Answer 2

Just noticed that Steve answered the same question when you reposted it just a few entries above this

Please avoid reposting the same question, especially when it still shows near the top of the list of questions like it did here.
It avoids unnecessary duplication of solutions.