What is the symmetric equation of a line in three-dimensional space?

1 Answer
Nov 20, 2014

The symmetric equation of the line with the direction vector #vec{v}=(a,b,c)# passing through the point #(x_0,y_0,z_0)# is:

#{x-x_0}/a={y-y_0}/b={z-z_0}/c#,

where none of #a,b# and #c# are zero.

If one of #a,b#, and #c# is zero; for example, #c=0#, then we can write:

#{x-x_0}/a={y-y_0}/b# and #z=z_0#.

If two pf #a,b#, and #c# are zero; for example, #b=c=0#, then we can write:

#y=y_0# and #z=z_0#

(There is no restriction on #x#, it can be any real number. )


I hope that this was helpful.