Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of (c) -E - 2F

Video transcript

Hey, everyone. So this problem is dealing with vector multiplication and addition. So let's see what they are asking us. So we have a magnitude of a new vector minus A minus three B when A and B are both given to us in their vector component forms. So we'll call this new vector V and we'll write that as minus A minus three B where A is I, we're gonna call that one I plus two J And B is one, I -2 J. So three B is going to be three times B and so we're going to multiply both the X and Y components by three. So we'll have three I minus six Jan. And so when we right out this minus A minus three B minus A is going to be minus one, I minus two J because the negative sign is for both of the X and Y components and then minus three B. So minus three I and then minus a negative is a positive. So it'll be plus six J. Well, some are eyes and rj's and we'll get negative for I plus four Jack. Recall that the magnitude of a vector is the square root of the sum of the squares. So the magnitude of this new vector V is going to be the square root of minus four squared plus four squared Plug that into our calculator and we get 5.66. So that is the correct answer for this problem. And that aligns with choice A, that's all we have for this one. We'll see you in the next video.