For this question we're getting to Curry X Plus Wife's were seen equals four and X equals one. And at that 10.1 comma, one common one. We're trying to find the Parametric equations of the line tangent to the intersection, the skirts. And so, uh so, first of all, let's right. It's created F of X y Z as X plus y squared plus C minus four and g of x y z b X minus one And so, essentially that if we think about the definition of the tangent line of these two curves, we know that the tangent line is perpendicular to both the Grady in of F and the Grady in a GI. That's how we that's how like the tangent line is formed, right? And so the tangent line must go in the direction. So if we have a line of the form, essentially the tangent line must be in the direction off. Radiant Death cross radiant G permit. And so we need to find greedy enough cross creating a G at the 0.1 comma one cover one. So, first of all, it's fine degree. Annabeth, Right. Sorry. The greeting of s is equal to 12 Why bottom and so the great enough as that 111 is equal to one common too common one. Likewise, the greening of she had it With respect. X Y Z is simply 100 And so the ingredient of G at one comma, one comma one is equal to 100 And so now we must try to find the cross product off great and F cross grading of G at one comma, one comma one. And so, if we do this and we work it out so I won't go, I'm just going to assume that we we know how to do cross products. It's not weaken. Go back earlier into the book and they do explain how to do cross products. But for the sake of time under, it's gonna, uh I'm just gonna sit to write to the cross border. Yet Syria too negative too. And if you are confused, ah, Or if you didn't get this, check your work. Yeah, and if not, just look back earlier in the book, they do talk about how to find cross buttocks. But essentially, once you find this, we know that essentially that the line will be of the Forum X is equal to x o plus the x component of this so plus zero t Why is equal toe? Why component the Y component of the given point plus two times T and then Z will be equal to the Z component, plus my plus negative to t. So since we know that at a given point is 111 you simply plug in and get the X is equal to one. Sorry, there's no there's no zero here. Why is equal to one plus two? T and Z is equal to one minus two t and that's our tangent line. So to recap, essentially, we're giving these two curves, right? We create these two functions and essentially what we do is we think OK, if we're trying to make a parametric equation of this function, we need to know the vector that defines the direction of this line. Right. If we're trying to be a parametric equations like a tangent line, we need to know like the direction off Mike essentially the vector that defines the direction in which this tangent line is moving. And so we think Okay, What direction will this doctor be in? Well, it has to be perpendicular toe the Grady int off the first function and stand in two. And it also has to be perpendicular to be Grady of the second function. That's tangent to. So that must mean that the vector itself must be in the direction of the cross product of these two Grady INTs. So once we realized that all that's left is for us to explicitly find this, um, after mentioned across product and I ah, since so we worked it out and we found that the cross product is this zero common too common Negative too. And Ah, yeah, You can check my work on the cross border. Essentially, After we do that, we just plug it into this equation, right? And then we get our desired parametric equations.