 In other courses you found the distance between two points. The distance between other objects is a little bit more complicated. We could introduce formulas, but we won't. Remember, learn concepts, not formulas. Instead, we'll use two strategies. Find the right triangle and use trigonometry. So let's find the distance between a point and a line given in vector form. Now the distance is the length of the perpendicular from the point to the line. If we make this one side of a right triangle, the hypotenuse will run from the point to some point on the line. If only there was some way to find a point on the line. Oh wait, we have the vector equation. So if t equals zero, then we have a point on the line. The vector from this point to the point on the line is going to be, and now we have one side of a right triangle. If only there was a way to find some other information, like the angle between two sides. Oh wait a minute, that's what the dot product is for. So we have the direction vector for the line, and the dot product will give us the cosine of the angle between these two. So we'll find the dot product, we'll find the norm of the vectors, and the dot product is the product of the norm times the cosine of the angle, so substituting in our values we find. Now if we look at our triangle, we note that the distance satisfies the length of the hypotenuse times the sine of theta. If only there was, oh yeah, no, we know how to find the sine of theta from the cosine, and so we get. So putting everything together, we have our distance between the point and the line. Now we could put everything together into a formula, we'll let you do that, but more importantly, this is one way to find the distance between a point and a line. It relies on the dot product in trigonometry, but there are other ways we can find the distance. We'll look at two other ways to find the distance, one based on calculus, and the other based on linear algebra.