Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. (c) v = (14i - 11j) m/s

Video transcript

Welcome back everyone. We are given this vector S right here and we are tasked with drawing the vector and marking the magnitude and direction. In order to do this, I'm going to go ahead and set up an X and A Y axis here for us to be able to do that. This is going to be our positive X direction and this is going to be our positive Y direction. Now, the X component of a vector is the numerical value multiplied with the I unit vector. So we know that it will go through the point that is 12 units out in the X direction and nine units up in the Y direction. So here is our 90.12 9 and we know that our vector will pass through that point there. This is our vector S and what this establishes is an angle theta with the positive X axis. And we need to find the magnitude of SS as well as that angle measure theta here. So let's go ahead and start out first with the magnitude of S, the magnitude of S is going to be given by the square root of the X component of S squared plus the Y component of S squared. What this gives us is the square root of, well, 12 squared is 1 44 plus nine squared, which is 81 giving us that the magnitude of S is 15 m per second. Wonderful. So now let's go ahead and move on to our angle measure theta. We have that theta. Well, what can we do to find theta we have that the tangent of theta is equal to the Y component over the X component. In order to isolate our uh beta variable, we take the inverse tangent of both sides. And what this gives us is that theta is equal to the inverse tangent of our Y component divided by our X component. Let's go ahead and plug that in. We have that the inverse tangent of our Y component nine divided by 12. When we plug that into a calculator is 36. degrees. So let's go ahead and scroll down here just a little bit to look at all of our answer choices. And the one that exactly matches ours is going to be answer choice. C Thank you all so much for watching. I hope this video helped. We will see you all in the next one.