# Thread: Parametric Equations for a Line

1. ## Parametric Equations for a Line

Given that a, b, and c are not all zero, find parametric equations
for a line in R3 that passes through the point (x0, y0, z0)
and is perpendicular to the line
x = x0 + at, y = y0 + bt, z = z0 + ct

2. ## Re: Parametric Equations for a Line

Originally Posted by Civy71
Given that a, b, and c are not all zero, find parametric equations
for a line in R3 that passes through the point (x0, y0, z0)
and is perpendicular to the line
x = x0 + at, y = y0 + bt, z = z0 + ct

Find any vector $\displaystyle <\alpha,\beta.\gamma>$ such that $\displaystyle a\cdot\alpha+b\cdot\beta+c\cdot\gamma=0$.

Then the line is $\displaystyle <x_0,y_0,z_0>+t<\alpha,\beta.\gamma>$.

3. ## Re: Parametric Equations for a Line

Originally Posted by Plato
Find any vector $\displaystyle <\alpha,\beta.\gamma>$ such that $\displaystyle a\cdot\alpha+b\cdot\beta+c\cdot\gamma=0$.

Then the line is $\displaystyle <x_0,y_0,z_0>+t<\alpha,\beta.\gamma>$.
such a vector is (0,0,1)X(a,b,c), which is perpendicular to (a,b,c)