One force acting on a machine part is F = (-5.00 N)i + (4.00 N)j. The vector from the origin to the point where the force is applied is r = (-0.450 m)i +(0.150 m)j. (a) In a sketch, show r, F, and the origin.

Video transcript

Hey everyone today, we're dealing with the problem about the Cartesian plane. So we're being told that we have A door and we're exerting a force at a point on the door with a position vector of two. I negative three J. With em being the unit of the vector. Or so. The vector is the position. So it's in meters with respect to the hinge. The exerted force has given any unit vector notation Where F is equal to 15 n. or 15. Newton, I -10. Newton. J. The hinge is located at the origin of the Cartesian plane. So we're being asked to draw the position vector R. The force vector F. And the origin. So I've already gone ahead and drawn out our plane here. I've put our origin as well. And before we get started, I'd just like to note that each of these units is two. So this will be two before 68, 10, 12, 14 and so on. So with that out of the way, let's just go ahead and take a look at this. So typically the directions of the position vector and the force are represented in the Cartesian frame. And we can say that the unit I I represents the positive X direction where a negative I would be the negative X. Direction. And similarly J represents the positive Y direction, negative J represents the negative Y direction. Let's go ahead and write that into, we have positive J. Positive I negative J and negative I. So going ahead with this with this logic, let's say we write the position vector R in blue. We can say its position if I. S. X. Is I I. Is the X axis and J. Is the Y axis. This position will be to negative three. And what does that look like? Well too is this first value here in negative three would fall somewhere between two and four. Right in the middle. So the position the position vector would fall as such from the origin. Just the position vector R. Let's go ahead and take a look at the force. The force is said to be 15. I -10J. Which is just 15 negative 10. Referred to think about this as X and Y. So 15. Well we established that this last one, this last marker here is 14, so 15 should fall just beyond that and 10 negative 10 will be 2468, 10. So it'll be somewhere around here. So let's go ahead and draw that into. And our arrow, that is our force. And there you have it were only representing the directions of the vectors. That's what's being asked here. So that'll be the graphic the position vector R. The force vector F. And the origin as represented in the Cartesian plane as shown above. I hope this helps. And I look forward to seeing you all in the next one