Equation of a three dimensional line

Using parametric equations in three space (n- space too if you can envision n dimensions).

The form of a line in three space has the general form
x = a1 + b1*t
y = a2 + b2* t
z = a3 + b3*t

which can be rearranged into another common form for lines in space

(x-a1)/b1=(y-b2)/b2=(z-a3)/b3

Another easy to looks at the geometry, a point in a plane is a intersection of two lines. And a line in a space is an intersection of two planes.

BTW the equation of a line in two dimensions (aka a1*x+b1*y=K) becomes a plane in 3 dimensions.

You might also look at A line in 3 Dimensions

Rap

Thanks Rap. Much Appreciated.