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Summary of Lines and Planes

Lines in 2D Lines in 3D Planes in 3D
Graph y = mx + b

m = slope
b = y-intercept
[ignore] z = Ax + By + C

A, B are slopes
C = z-intercept
Parametric L(t) = p0 + tv

p0 = (x0,y0) = point on L
v = <a,b> = direction vector

Coordinate form:
x = x0 + at
y = y0 + bt
L(t) = p0 + tv

p0 = (x0,y0,z0) = point on L
v = <a,b,c> = direction vector

Coordinate form:
x = x0 + at
y = y0 + bt
z = z0 + ct
P(s,t) = p0 + tv1 + sv2

p0 = point on the plane
v1,v2 = non-parallel vectors
lying in the plane
Implicit ax + by = c

N = <a,b> = normal vector
c = N.p0 for p0 a point
on the line
[ignore] ax + by + cx = c

N = <a,b,c> = normal vector
d = N.p0 for p0 any point
on the plane


[HOME] Math 15 (Winter 2001) web pages
Created: 13 Feb 2001
Last modified: 08 Mar 2001 20:25:10
Comments to: dpvc@union.edu
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