There is three major forms of linear equations:
- vector form: (x,y,z)=(x0,y0,z0)+t(a,b,c)
- parametric form: x=x0+ta,y=y0+tb,z=z0+tc
- symmetric form: ax−x0=by−y0=cz−z0
Where x0,y0,z0 - point on that line
(a, b, c) - directing vector of a line
t is a parameter, t∈R
(a, b, c) = (1 - 2, 4 - 1, -3 -3) = (-1, 3, -6)
Then
- vector form: (x,y,z)=(2,1,3)+t(−1,3,−6)
- parametric form: x=2−t,y=1+3t,z=3−6t
- symmetric form: −1x−2=3y−1=−6z−3
Comments