List of formulas related to Analytic-geometry (Line in 3D)
Line forms
Point direction form:
x−x1a=y−y1b=z−z1cTwo point form:
x−x1x2−x1=y−y1y2−y1=z−z1z2−z1Parametric form:
x=x1+tcosαy=y1+tcosβz=z1+tcosγDistance between two lines in 3 dimensions
The distance from | P2(x2,y2,z2) | |
to the line through | P1(x1,y1,z1) | |
in the direction | (a,b,c) | is |
The distance between two lines.
First one: through | P1(x1,y1,z1) | |
in direction | (a1,b1,c1) | , |
Second one: through | P2(x2,y2,z2) | |
in direction | (a2,b2,c2) | is: |
The two lines intersect if:
|x2−x1y2−y1z2−z1a1b1c1a2b2c2|=0