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
3D Line Equation Forms
Parametric
x = x₀ + at
y = y₀ + bt
z = z₀ + ct
Symmetric
(x-x₀)/a = (y-y₀)/b = (z-z₀)/c
Vector
r = r₀ + td
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun