Parametric Equations of a Line
Main Concept
In order to find the vector and parametric equations of a line, you need to have either:
two distinct points on the line
or
one point and a directional vector.
A directional vector, m, where m = a, b, is a nonzero vector parallel to the line. The directional vector can be represented by a vector with its tail at the origin and its head at point (a , b).
In the first case, you can obtain a directional vector by subtracting the two given points.
The x and y components of vector m are called direction numbers.
Vector Parametric Equation:
Scalar Parametric Equations:
r = r0 + t ⋅ m
x = x0 + t ⋅ a
y = y0 + t ⋅b , t∈ R
r0 is the vector connecting the origin to a point x0 , y0.
m is the directional vector with the directional numbers a ,b.
Click or drag the directional vector and a point on the line. Select the check box to show the resulting line.
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