Is there a point slope form for a three dimensional line?

1 Answer
Dec 19, 2017

Not really, but...

Explanation:

Something vaguely similar that you can use for a line in any number of dimensions is a point-vector form, which you could write like this:

#underline(x) = underline(x_0)+tvec(v)#

In three dimensions:

#(x, y, z) = (x_0, y_0, z_0) + t(u, v, w)#

#= (x_0 + tu, y_0 + tv, z_0 + tw)#

where #(x_0, y_0, z_0)# is a point through which the line passes, #(u, v, w)# is a vector describing the direction of the line and #t# is a parameter ranging over #RR#.

If #(u, v, w)# (or in more generality #vec(v)#) is of unit length, then the parameter #t# acquires extra meaning in being the distance along the line from the fixed point.