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+#rs/notes #rs/class/math163
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+- 3D lines
+	- can be described as parametric
+	- symmetric equation of 3D line $$ \frac{x-x_{0}}{a} = \frac{y-y_{0}}{b} = \frac{z-z_{0}}{c}$$
+	- In this case, the direction vector is $<a, b, c>$
+- Distance between a point and a line
+	- Is the shortest distance between the two
+		- This is the segment perpendicular to the line
+	- In 2D, you have to take random point on the line
+		- then project vector from this point to point not on the line onto the line to find where the closest point on the line is
+		- ![[Pasted image 20251014183240.png]]
+		- In this parallelogram, we know the area is equal to either $v \times PM$ or the base * the height (the height is the distance beween M and the line
+		- This gives the formula $$d=\frac{||PM \times v ||}{||v||}$$ For the distance between point M and the line
+- Lines in 3D
+	- Can either be parallel, intersection, the same line or skew
+		- skew is when they don't intersect but aren't parallel either
+- Planes in 3D
+	- defined by the normal vector of the plane