the dot product done wrong....

every semester I tell people they're going to make this mistake, and every year they go ahead and make this mistake:

done wrong:

<-2,3,3>.<1,-1,4>=<-2,-3,12> 

🙀😐

and done right:

<-2,3,3>.<1,-1,4>=(-2)x1+3x(-1)+3x4=-2-3+12=7