Find the Area of the Parallelogram

[Lurid]

Homework Statement

Find the area of the paralellogram with vertices P₁, P₂, P₃, and P₄. *Not all pairs of vertices will give rise to a side.

P₁ = (1, 2, -1)
P₂ = (4, 2, -3)
P₃ = (6, -5, 2)
P₄ = (9, -5, 0)

Homework Equations

||U X V || is the area of the parallelogram having U≠0 and V≠0 as adjacent sides.

The Attempt at a Solution

How do you know which set of points will create a vector that are adjacent to each other?

 

[HallsofIvy]

You are told that this is a parallelogram- opposite sides must be parallel to one another.

 

[LCKurtz]

And usually such problems give the points going around the object. So if it is a parallelogram and the points aren't mixed up, you might expect $P_1P_2$ and $P_3P_4$to be opposite sides. Of course, you would have to check to see if those two sides are parallel to see if that is true...