It's exercise. We have a professor that drives 3.25 kilometers north. Then he drives for 0.75 kilometers west and won't wait five. Killing herself and Argo is to calculate what is the final total displacement off the professor, The net displacement and the direction the way she drove s so basically what I'm gonna do is to consider each leg of his journey as one vector. So I'm setting gonna set up a cordon system such that the Y axis points to the north and the accesses point points to the the east such that the, uh, trajectory of the professor is compose off three point 25 kilometers north. It's this vector that points in the Y direction, then four point, and I'm gonna, uh, write it in the origin. So we have the vector of 4.75 kilometers to the west and finally the vector of 1.5 kilometers to the south. So the first vector I'm gonna call it the one. It's 3.25 j kilometers de to is equal to minus 4.75 I kilometers. Indeed, three is equal to minus 1.5 Jake lovers in the total displacement is equal to the sum of these three legs of the journey. So the warm was the 2003. So we get three points 25 miles, 1.5 j minus four points. Have any five I cologne letters. And just to write it in a more usual form, this is able to minus four point 75. I close 1.75 j kilometers. And with this information working right, you can find the magnitude of the displacement that's the square root of DX swear. So it's 41 75 square was de y square. So it's 1.75 spared. So d is equal to 5.0, six kilometers. And we also want to find the direction of this vector notice that the better D has a negative X uh, a component and a positive white important. So it's pointing in the second quadrant, and we want to find the angle that it makes with the horizontal. So we want to find this angle here. Fada, In order to find data, I'm actually gonna find this angle phi here and use that data plus five. It equal to 180 degrees. I noticed that later the attention off there will be able to de Why the momentarily Why divided by the manager of the X. So we get that 10 Geant off theatre is the magnitude of the wider. But it was elected D X so fine is equal to the ark tensions of the magnitude of the Y, which is 1.75 to write about the magnitude of D X, which is 4.75 and this is equal to 20.2 degrees. So Fada is equal to 180 minus two any point to which is 158.8 degrees. And this is the direction, uh then have to draw the diagram and show that ah ah, the diagram agrees qualitatively with the result we found so basically again, I'm setting up, uh, corn and system here and initially, the professor drives three point 25 kilometers north. So this is people in kilometers. Then he drives four 0.75 kilometers west and finally he dries 1.5. So So this is about 25 kilometers, please. Daughter displacement is the vector that connects the origin with the final point, which is this vector here. Notice that it still points in the third quadrant as we wanted to. Okay, and I noticed that it is necessarily bigger. It's in magnitude. It's greater than magnitude, then 4.75 kilometers. Eso It's consistent with the fact that the displacement, the magnitude of this waste minutes 0.5 point off six kilometers and this concludes our exorcists.