In two-dimensional space, we can represent a line using an equation like y equals mx plus v. In three-dimensional space, an equation like that doesn't work because it ends up describing a plane of space rather than a simple line. And so we need something else. So let's suppose I have a point out here, x not, y not, z not. And I have a direction that my line is going to travel in. So let's imagine I have a vector on this line and we'll call it the vector v. So we've got a point on space, we've got a vector pointing in the direction of the line or parallel to the line. So we're going to introduce, let's imagine that we have the origin down here somewhere. We're going to introduce a position vector, a vector from the origin out to this point and we'll call it r not. Then any point on the line can be represented as the sort of end of a vector r. Where that vector r is the original r not point plus some scaling of the vector v, right? Because this of v r not plus one v, this might be r not plus two v, three v, four v. So we're combining this vector r not with scaling of that vector v. And if we scale that vector v by t, then any vector r pointing to some point x, y, z on the line can be represented as r not plus t times v. Now in some cases this vector formable line is not horribly convenient. So we could break this down and say the vector v is the vector pointing to x, y, z. So it is the position vector x, y, z, right? This would be the vector from the origin out to x, y, z. The vector r not here is x not, y not, z not. And let's say the vector v has components v sub x, v sub y, and v sub z. Then here's a more written out vector form. And then we could scale this vector and combine the components here to say this is x not plus t v sub x, y not plus t v sub y, and z not plus t v sub z. Now because this vector is equal to this vector, the x component of a point on space can be represented using this expression y and z the same. And so we can end up writing a set of parametric equations that are equivalent to this vector equation. We can say x of t is x not plus t v sub x, y is equal to y not plus t v sub y, and z is equal to z not plus t v sub z. And this set of parametric equations is equivalent to this vector equation for a line. So we can write an equation of a line in three space using either of these two formats.