3D Line Equation Calculator

Find parametric, symmetric, and vector forms of a line in 3D space.

Input Method

Point P₁

Point P₂

Parametric Form

r(t) = (1.00 + 3.00t, 2.00 + 3.00t, 3.00 + 3.00t)

Vector Form

r = (1.00, 2.00, 3.00) + t(3.00, 3.00, 3.00)

Symmetric Form

(x - 1.00)/3.00 = (y - 2.00)/3.00 = (z - 3.00)/3.00

Direction Vector

d = (3.0000, 3.0000, 3.0000)

|d| = 5.1962

d̂ = (0.5774, 0.5774, 0.5774)

Distance from Origin

1.4142

Closest Point to Origin

(-1.0000, 0.0000, 1.0000)

Points on Line

t=-2(-5.0000, -4.0000, -3.0000)

t=-1(-2.0000, -1.0000, 0.0000)

t=0(1.0000, 2.0000, 3.0000)

t=1(4.0000, 5.0000, 6.0000)

t=2(7.0000, 8.0000, 9.0000)

t=3(10.0000, 11.0000, 12.0000)

Parametric

x = x₀ + at

y = y₀ + bt

z = z₀ + ct

Symmetric

(x-x₀)/a = (y-y₀)/b = (z-z₀)/c

Vector

r = r₀ + td