This exercise. We have a trapper Woakes, a distance of five kilometers with ah direction off 40 degrees to the north of the X axis. And what we have to do is to calculate the components of the displacement vector off the trapper. So let's do it. The displacement vector is this blue vector here, Um, with a magnitude of five kilometers, I'm gonna call the displacement vector A. So A is equal to a axe, which is the X components times the unit vector in the X direction I plus a why j which is the unit vector in the white? Yeah, direction. So a X is equal to the magnitude of a times the co sign of 40. So this is equal to the magnitude of a is five kilometers times the call sign of 40 which is equal to 0.766 and a X is equal to 3.83. A y is equal to the magnitude of a times the sign of 40. So a why is able to five loners times 0.6 for three, which is equal to three points 20 work. So the total factor is equal to 3.83 i plus zero after three points. 21 j kilometers. What? Okay, Then we have to calculate how how many more kilometers this trapper would have to walk if she chose to walk in a straight line along acts direction and then in a straight line along the wide rash. In that case, the total dis and she traveled would be a total distance would be the X component a X plus the y component A Why this is 3.8 e three plus 3.21. So this is equal to 7.4 This is the total distance you would have to travel. And since when she walks in a straight line, she travels only five kilometers and the difference in the distance don't A D is equal to two point 2.4 kilometers. So she would have to vote 2.4 cloners more then she does. Ah, and finally we have to say what is her displacement of actor? So notice that either way Ah, this matter If she she walks straight to the finishing point or if she Woakes first, uh, along the X axis and then along the y axis, uh, along the y direction? Sure. Ah, her displacement vector will be the same because of this basement. Vector is the vector that connects the starting point in the finishing point, regardless of the trajectory. So her displacement vector would still be the defector with magnitude of five kilometers with an angle of 40 degrees with the X axis, and for the reason her despite displacement vector would still be 3.83 i plus 3.21 j kilometers.