3D Line Equation Calculator
Find parametric, symmetric, and vector forms of a line in 3D space.
Input Method
Point Pβ
Point Pβ
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
dΜ = (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)
3D Line Equation Forms
Parametric
x = xβ + at
y = yβ + bt
z = zβ + ct
Symmetric
(x-xβ)/a = (y-yβ)/b = (z-zβ)/c
Vector
r = rβ + td
π‘
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