Vectors: Lines, Planes, and Parametric equations

Lines and Planes

y = 3x + 4 + (0z)?

I have no idea what this looks like!  Until you tell me how many dimensions there are...

lines; == is ugly... so lets do parametric equations! (in 3 dimensions)

x = p_1 + v_1t
y = p_2 + v_2t
z = p_3 + v_3t

p = point
v = vector!

Look for the vector!

n < vector normal to the plane


Planes
ax +by +cz = d

a,b,c coefficients  = normal vector
d = normal vector (dot) point

Cross product of the vectors lying in the plane!

Set t = 0 to find the constant on the line!
Coincident = same line

Skew = one line is above the other in 3D

Distance from a point to a plane
from p to plane: abs[(d - vec_p (dot) vec_n)/||vec_n||]


ax + by + cz = d
vect_p