Finding a vector perpendicular to a plane

[Miike012]

How did they know to do PQ cross PR instead of PR cross PQ?
And why did they not choose RP cross RQ?

Look at picture.

 

[Mark44]

How did they know to do PQ cross PR instead of PR cross PQ?

Since any vector that is perpendicular to the plane will do, it doesn't matter if they calculate PQ X PR or PR X PQ, which will just point the opposite direction.

And why did they not choose RP cross RQ?

Look at picture.

If you cross any two vectors in the plane that aren't parallel, you'll get a third vector that is perpendicular to the first two.

 

[Miike012]

Another question:
if I have 3 vectors u,v, and w
If i am trying to find u cross v cross w do i cross u with v first then w or v cross w then u?

 

[Mark44]

I'm pretty sure they associate left-to-right, so u X v X w would be the same as (u X v) X w.