(a) Show that $ i \cdot j = j \cdot k = k \cdot i = 0 $
(b) Show that $ i \cdot i = j \cdot j = k \cdot k = 1 $
a) $i \perp j, j \perp k,$ and $k \perp i$
Okay, so I'm going to show that we can write I as the as a vector one zero zero j as the vector zero one zero and chaos the vector zero zero one. All right, so now it's just a matter of doing these dot products. So let's just look at one and then I'll let you kind of figure out the rest, right? So if we're going to do one time zero plus zero times one plus, you're in time zero, we always see that if these two vectors are different, then we're always going to match up a zero with something else and always get zero. Okay, so this makes sense. And if we look at these guys here, would you I with eye, we're always going to get the two components with the ones to match up and in the zeros with zero. So we always get one. Okay, that's the same with the J and the cakes of the ones. We're just in different places.