 In this video, we'll provide the solution to question number three from the practice midterm exam number two for math 2270 We are given three sets of vectors and we're asked to determine which of these ones or orthogonal So some things to remember about orthogonal sets is the orthogonal Orthogonal sets cannot contain zero which if I look for r s and t that's a quick thing to throw out here There's our no zeros. It knows no zero vectors anywhere. So I can't use that to throw anything out Also, if an empty set in a set of just a single non-zero vector always Orthogonal there's none of those present. So I'm gonna have to actually check pair by pair. What's going on here? So if you look at the first pair If you look at the dot product there, you're gonna get zero plus one plus one, which is two Which is not zero. So that tells us that r is not an orthogonal set because the first pair wasn't even orthogonal If you look at s we look at the second pair right here You're gonna get zero minus two plus two which is equal to zero. That's promising if you look at the second pair You're gonna get zero minus two plus two, which is zero. That's good Then we have to look at the third pair right here. We're gonna get minus five plus four plus one That's zero. So all three pairs are orthogonal. There's no zero vector in there So s is definitely gonna be a Orthogonal set let's do the same thing for t If we look at the first pair take their dot product you get zero plus one minus one. That's a zero. That's a good side The next one you're gonna get zero minus three plus zero That's equal to negative through which is not zero. So t is not an orthogonal set So the correct answer for this one would be b s is the only orthogonal set provided