So um We have the vectors V. W. And you and we had a. U. Is equal to the unit vector of B. Plus unit vector of W. And so having that, we need to show that the angle between you and me. They called to the angle between you and W. It's like. And the first thing I'm going to do is to show that the angle between you and me that is a call to the angle between you and um union victor bobby. And also we have that the angle between you and W. It's going to be equal to the angle between you and unit vector W. And that makes sense because the angle between you and W is the same as you and the unit vector of W. Because the unit vector W is the same direction. Just smaller. All right. So um first purpose now since the unit vector we and W are the same land. If I show that I knew that you need victory is equal to you. Dot product. You need victor. W. If I prove this that that means then that proves what we need to prove. So let's do so let's rewrite you as the you need vector formation of it. So, this is for the first one. And for you dot union vector W. We have this like getting inspector. We plus union victor. That will you multiplied by? Well, technically dot I forgot to put the dog product here. Adult. You need victor at W. All right. For the top one, you're gonna have unit vector V times T. V. Which is just one boss. You need victor. W thoughts. You need victor. Me. And for the bottom one, we're gonna have you need vector V. At times a unit vector W. Plus one. So, as you can see, these two are the same. Uh therefore the angle between U. And V. He recalled to angle between you and W. So we have a crew. That why that's the case. But let's look at it also geometrically, so geometrically, let's say this is me and this is w it really doesn't matter which ones they are. I just arbitrarily say they're these ones. And so what is the unit vector of B? Let's say this is the unit vector of we and this is a union victory of W. So they had the same length. Therefore for you, She's going to be the addition of the two. We can see that. Um This is gonna be you right here and as you can see the angle, the angles are the same. This angle between you and we looks about the same as a single between U N W. And that is the case because right here, if I circle it in red, this is going to be um like a kite, which means all the sides are the same length, which kind of proves that the angles are also the same, and so every time.