1.0 KiB
1.0 KiB
#rs/notes #rs/class/math163
- 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
- !
- In this parallelogram, we know the area is equal to either
v \times PMor 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
- Is the shortest distance between the two
- 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
- Can either be parallel, intersection, the same line or skew
- Planes in 3D
- defined by the normal vector of the plane
