Math 203 Lecture 6 - Equations of lines and line segments in 3D

In today's lecture, we first go over homework regarding the cross product. We then quickly jump into the main meat of the lecture.

We cover the equations of lines in 3D. There are some similarities to how we found lines in 3D, but also some significant differences. We still need linear forms, but now, they become components of vector functions. We derive the equation of a line, and derive three forms: first the vector form for the equation of a line, followed by the parametric and symmetric forms of the equation of a line. We also look at line segments and how to find them. We look at what makes two lines parallel or orthogonal (perpendicular), and show how to determine if two given lines are parallel, intersecting or skew (not parallel nor intersecting). We will look a bit more at the equations of lines in a week, and then move on to the equations of planes in 3D.

[countingpebbles]

Why not solve using gauss-Jordan elimination! It becomes apparent immediately that the trivial solution exist. System would be inconsistent if not point of intersection existed. Also, would have atleast one row of zeros if the system is consistent. Anyway, great video, I was watching another series in calc 3, but I have jumped over towards this one as it is far better. I find it to be fruitful to learn calculus 3 using areas from linear algebra and differential equations. Unfortunately, they are not intertwined as I was hoping, since most students take this concurrently those subjects or don't at all. Anyway, looking forward to the rest of the series. Thank you.