Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (a) B = -4.0i + 4.0j

Video transcript

Welcome back, everyone. We are given this vector M right here and we are tasked with finding drawing the vector and showing the direction of the vector very clearly. So to start out here, first, what I'm gonna do is I'm going to draw an axis here for which we can go ahead and draw out our vector given the X and Y components here. So as you can see what's multiplied with the I unit vector is gonna be our X component and what's multiplied with the J unit vector is going to be our Y component. So according to our vector M, it is in the direction of negative three X and positive three Y at the point negative 33, that is where we are going to have our vector M through. This will be our vector M. And then we have some angle measure theta here. But we want to find what the magnitude of our vector is as well as what the angle measure of theta is as well. So let's actually start out with the magnitude of M what is going to be the magnitude of M. Well, that's going to be given by the square root of the X component of M squared plus the Y component of M squared. When we plug this into our calculator, what we get is the square root of negative three squared is nine plus three squared is also nine giving us the square root of 18, which is about 4.24. Wonderful. Now that we have that we are ready to find our angle measure beta. Here we know that the tangent of theta is just going to be the Y component of our vector divided by the X component of our vector. In order to isolate our theta variable, we are going to take the inverse tangent of both signs. Now, what that gives us is that theta is equal to the inverse tangent of M Y O over M X. So let's go ahead and plug in our values here. What we are going to get is the inverse tangent of three divided by negative three which gives us negative 45 degrees or 45 degrees above our negative X axis. So we have that this is 45 that the magnitude of M is 4.24 which corresponds to our final answer. Choice of B. Thank you all so much for watching. I hope this video helped we will see you all in the next one.