Given two vectors A = 4i + 7j and B = 5i - 2j, (a) find the magnitude of each vector;

Video transcript

Welcome back everybody. We are given two vectors and we need to determine the direction of the vector. B minus a. Well, first and foremost let's calculate what B minus A is now to do vector subtraction. You just do it component wise. So it will simply be B x minus b x minus a. X X. Component plus B y minus a. Y. Let's go ahead and plug that into your b minus A. Is equal to six minus three. Three plus 8 -4 which is four. Now that we have B minus A. We can use the formula that tangent data is equal to the Y component divided by X. Component. In order to find data, I'm going to take the arc tangent of both of these sides to isolate our theta. And this yields that the arc tangent of B. Y, which is four divided by three, is equal to our theta. When you plug this into your calculator, you get 53.13 degrees, which corresponds to our final answer of B. Thank you guys so much for watching. Hope this video helped and we will see you all in the next one.