Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.

〈5, 7〉

Video transcript

Welcome back everyone in this problem. For the given vector 1114, we want to calculate its magnitude and direction angle. We want to express our answer to the nearest 10th as well if required for our answer choices. A says the magnitude is the square root of 317 and its direction angle is 51.8 degrees. B says it's 317 and 51.8 degrees respectively. C says it's the square root of 317 and 94.8 degrees. And D says it's 317 and 94.8 degrees respectively. Now, first, let's visualize what's going on here. So we have a vector 1114. OK. And on our X and Y axis, it would probably look something like this. OK? Where its length, its length is 11 units and the X axis and its height and the Y axis is 14 units. And what we're trying to do is to calculate its magnitude that is its length. And we're also trying to figure out its direction angle that is theta here in our diagram. So how can we figure it out what do we know about magnitude and direction angles of a vector? Well recall now the magnitude of A vector D is equal to the square root of A squared plus B squared are the sum of both the sides are the sum of the shorter side. Rather, it's X and Y components. And we also recall that our direction on the theater would be equal to the arc tangent of B divided by A. So here where A represents its X component and B represents its Y component. And since A equals 11 and B equals 14, we can substitute those values for A and B to eventually find their magnitude and direction angle. OK? Because no, this tells us that B is gonna be equal to the square root of 11 squared plus 14 squared. OK, which would be equal to the square root of 11 squared 121. While 14 squared is 196 and 121 plus 96 equals 317. So the magnitude of our vector is the square root of 317. Likewise the angle its direction and the, theta is going to be equal to the inverse tangent of 14 divided by 11. And in this case, the inverse tangent of 14 divided by 11 equals 51.8 degrees to the nearest 10. Therefore, the magnitude of our vector is the square root of 317. And its direction angle. Is 51.8 degrees. If we look back on our answer choices. A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.