All right, we've got a question about someone running 100 m dash on a track in the direction of the vector V equals to two. I waas six check, all right. And we're told that the wind velocity it's equal to five. I loss she to jail kilometers per hour. And we're told that the rules were saying that the legal wind speed is measured in the direction of the dash must not exceed five kilometers per hour. Well, when they were asked to answer, what was the race results be disqualified due to an illegal went So essentially, I guess in order to make the race fair, they've set certain rules in place to ensure that the wind does not become a substantial factor and influence in the race. And they've deemed that to be the speed of five kilometers per hour. All right, so basically what we need to do here is just solve for the speed of the wind. If we consult for the speed of the wind and then we can see if it's greater than a less than five kilometers per hour and we'll know whether or not it pulled a substantial, uh, factor in determining whether or not this race is to be disqualified or not. Okay, so whenever we're solving for the speed or the velocity when were given a vector, we take the dark products and we divide that by the magnitude. Eso you do You gotta be over. Um, the magnitude Okay. In this case, are you is going to be our wind. Okay, so our w dot be over the magnitude our be here, which would be to I for six years and basically replicating the the equation. Just my attitude. Okay, Now the answer here will be you have five times two just 10 and then 10 plus 12. So we have at the top 22. Take the dog product and then the magnitude here would be square root of two squared plus six square No. Two squared is 46 squared is 36 four plus 36 is fourth, right? And then you go ahead and plug this in into your handy dandy calculator. We'll get the answer. 3.4 eight. We can see that 3.48 kilometers per hour is clearly not greater than five kilometers power. So we can confirm that the wind will not be a substantial factor in the race. Therefore, the race, the race results its salts stand this so they stand perfectly fine and the race is not this horrible or the race results. Excuse me, are not going to be this world or in in order to solve this question just to clarify We took the window back during the philosophy that term we need to find speeds. We went ahead and, um took the dot product over the magnitude led to our speed and they found that it was less than five kilometers per hour. Therefore, race results stand and the race results were not disclosed. I hope that clarifies the question. Thank you so much for watching.