Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (b) r = (-2.0i - 1.0j) cm

Video transcript

Welcome back, everyone. We are given the following vector P and we are tasked with labeling the magnitude and direction on a diagram of our vector here. So first let's go ahead and draw out our vector. I'm gonna go ahead and make a little graph for us so that we can accurately plot both of our components of our vector P. So what are we given here? Well, for the first half of our vector, we have that the I component will be represented in the X direction and the Y J component will be represented in the Y direction. So what it's telling us is that we go negative four points in the X direction native X direction and we go six points in the negative Y direction or six increments here. So that means there's going to be a vector connecting the point we just marked negative four, negative six and the origin here. So let me go ahead and draw that vector like. So, so this is what our vector is going to look like, but we still need to find what that angle theta is as well as what is going to be the magnitude of our vector P. So we have to find the magnitude as well as the angle measure for theta. Let's go ahead and start out with the magnitude of our vector. Here's how we're going to find this. The magnitude of our vector is given by the following formula. We have the square root of P X squared plus P Y squared. Where P X and P Y are the individual X and Y components. What we have here is negative four squared is 16 plus negative six squared is 36. And when you plug this in your calculator, we get a magnitude of 7.21 newtons. Wonderful. So now let's go ahead and move on to that angle measure of theta here. How are we going to find the, well, we can say that the tangent of theta is equal to our Y component of over our X component in order to isolate our theta variable. What we are going to do is we are going to take the inverse tangent of both sides of our equation. And what you'll see is that this gives us that theta is equal to the inverse tangent of our Y component over our X components. So let's go ahead and plug in our numbers here. We have that the inverse tangent of negative six over negative four, which is is 6/4 four. Gives us when we plug into our calculator. A theta angle of 56.3 degrees. So now we have our diagram off to the left here. We have found our magnitude and our angle measure, which therefore is our final answer. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.