Okay, so this one has four parts, so? Well, go ahead to start with a here. Um, we need to figure out what are these actors orthogonal Kyle? Or neither. So for party, we have vector a being equal to negative five, three and seven and a vector B is equal to six. Negative eight and two. Okay. So to determine if they are perpendicular, we want to find their dot product. So a dot B is going to be equal to negative five times six plus three times negative, eight plus seven times two. And this is negative 40. And this does not equal zero. So therefore they are not perpendicular now. If they were parallel, then there would be some sort of scaler. Such that is equal to some scaler time, Inspector B. So to term in this, I think what would six need to be multiplied by to be equal to negative five, right, So six times negative 5/6 would give me negative five. So what happens if I multiply a negative eight by the same thing? If I were to take negative eight and multiply it by native 56? Well, that does not equal three. Right? So therefore, that's killer does not exist. Okay, so these are not parallel? Yes. Is the answer here then is going to be neither Neither perpendicular or parallel. So moving on to part B this time were given Vector A is equal to 46 and vector B is going to be equal to negative three two. So start by taking the dot product, and that is equal to four times negative. Three plus six times two plus zero time zero. So that's gonna give us negative. 12 plus 12 0 Awesome. So that means that they are perpendicular, okay? And we want to take a look and see if we can find some scaler such that a is equal to a scale air times be. And so what would we need to multiply? Negative three by to get four. So if I were taking be would need to be four divided by a negative three. Right? Would give me four. So if I multiply to buy this same four over negative three No, this this is gonna give me native thirds, which does not equal six s. So therefore, there is no no scaler that that does that on. So that means it's not parallel. So yes, perpendicular, but not Kayla. Okay, so we move on to part. See here Vector is equal to negative one, two and five, and the vector B is equal to 34 negative one. So to determine if they're perpendicular will take a look at the dot product that's gonna be equal to negative one times three plus two times four plus five times negative one that's gonna give us negative three plus eight minus five, and that is equal to zero. Okay, so that means that they are indeed perpendicular. And then we want to see if to be fair, once you know they're perpendicular, you know that they are not parallel. Um, but to be thorough, you know, Ah, doing the process of determining whether or not they are. We can go ahead and see if there's a scaler such that is equal to a scale or times be. And to do that we say what we we multiply times three to get negative one, and so he would take negative three. I'm sorry. Just take positive three, and we would multiply that fire and negative 1/3 So then we'll take this negative 1/3 and multiply it by four. And we would get negative 4/3 which does not equal to. And so it's not parallel. Yes. So for this one, we have again just a perpendicular hair vectors and on to Part D. The final installation. Here we have Vector a being equal to two six, negative four and vector be being equal to negative three, negative nine and six And so first to determine whether or not they are perpendicular we take the dot product and that would be equal to two times negative. Three plus six times negative, nine plus negative for times six so that it's gonna be negative. Six minus 54 minus 24. So negative 84. Okay, so then we know it is not perpendicular. So now we'll take a look and see if we can find a scale where a is equal to some scaler times be So what will we multiply by? Negative three to get to Well, that would be a negative 2/3. Okay, So what happens if we take negative nine and multiply that by a negative 2/3? Then we get six Okay, well, that equals the second element. A. So that's promising. So let's take six and multiply that by a negative 2/3. And what does that get? Well, that gives us a negative four. Okay, that minds Oppa's well. So the scaler is negative 2/3 and that means that he's won. Thes vectors are indeed parallel.